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Main
Date: 06 Oct 2007 21:55:02
From: foot
Subject: Counting knight moves
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Quick! What's the minimum number of moves a knight on g6 needs to get
to e4 ?
To answer this question, most chess players will simply start to
mentally move their knight around, counting the moves, until it lands
on the desired square. Let's say you counted 4 moves: e5-g4-f6-e4
That's one way to get there, and so is: f8-e6-g5-e4. But is there a
shorter route?
To answer that question with some measure of certainty (as opposed to
just guessing), most chess players would need to try a number of
alternate paths to e4. This might take an inordinate amount of time in
a game, and when the player has the answer, they might even need to go
through the moves again to double-check their answer, taking even more
time.
And what if the player was interested in more than one destination
square for the knight, or in the minimum number of moves it would take
for knights starting from two different squares to reach the same
square? Depending on where that square was, coming up with an answer
you felt confident in could really take a long time and be very
error-prone using the ordinary method of counting knight moves.
Fortunately, there's a better way. I'm a fan of obscure chess books, so
when I was at a local chess store the other day, the book "Knight
Moves" by Charles Alexander caught my eye. In it he describes a
relatively simple method, which he calls "Alexander's Technique", to
count the minimum number of knight moves it would take a knight to move
from any given square to any other square.
Alexander's Technique consists of a number of rules-of-thumb which the
player would need to memorize and apply. The rules range from the
incredibly simple -- such as learning that the only times it would take
a minimum of 6 moves to get a knight from one square to another is if
the knight starts on one of the corner squares (a1, a8, h1, h8) and
wishes to go to the diagonally-opposite square (ie. from a1 to h8, h1
to a8, etc...) -- to a number of more complex (but quite easily
learnable) rules.
It only took me a few minutes to start applying the rules after I'd
read the book, and maybe another ten minutes to half an hour to
completely internalize them... and after an hour or so of practice, I
feel completely confident I'd be able to quickly (certainly under about
15 seconds, and often as little as a second or two) to figure out what
the minimum number of moves it would take for a knight to get from any
one given square to any other.
The method can also be used to determine the minimum number of moves it
would take a knight to get to groups of squares. For example, if the
knight is **not** on one of the corner squares, you immediately know
that the minumum number of moves it would take to get to any other
square can not be greater than 5. The minimum number of moves it would
take a knight to move to other groupings of squares, such as any black
or any white square, could also be easily counted.
Alexander's Technique does have its limitations, the most obvious one
being that the presence of other pieces on the board might delay or
completely stop the knight from reaching a given square in the minimum
number of moves. For example, some moves might be illegal given the
situation on the board at a given time (such as having a piece of the
same color as the knight block one of the squares the knight needs to
move to), or if the knight gets captured on its way, etc... In this
case, the player is pretty much on his own in taking account of these
possibilities. Still, he can be certain that the knight will not reach
the destination square in less than the number of moves Alexander's
Technique tells him it will.
Another limitation is that the player could still make a mistake in
applying Alexander's Technique, perhaps requiring a double check of
some sort (by either re-applying Alexander's Technique, or manually
counting out the moves).
Still, given what Mr. Alexander set out to achieve with his method, I'd
say he admirably reached his goal.
One other thing that I should mention is that this is a really thin
book. All together it's only 82 pages, about 20 of which are exercises,
answers, and the index. Also, if you're just interested in learning the
technique itself, without knowing why it works, you could probably skip
the first 40 pages. And, if we also omit the 7 pages of examples of the
technique in action, that only leaves about 8 pages that you'd have to
read to learn the technique.
Of course, mastering the technique will require practice, so I advise
going through the examples, and doing at least 6 to 12 of the exercises
(which shouldn't take you more than an hour or so). After that, you'll
be counting knight moves like a pro! :)
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Date: 12 Oct 2007 22:10:14
From: foot
Subject: Re: Counting knight moves
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On 12 Oct 2007 14:18:33 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> foot <[email protected]> wrote:
> >>> As I've said several times now, the part of the book that teaches
> >>> the method only takes up 8 pages!
> >>
> >> This is obviously some strange new meaning of the word `only' of
> >> which I was previously unaware. Mine took less than half a page.
> >
> > Yes. And yours isn't even half as useful.
>
> In what way? It does exactly the same thing.
The method you describe is not (in my experience) as reliable, as
quick, or as free from the possibility of confusion. So, lacking these
qualities is what makes the method you describe not even half as useful.
> > Not to mention that you didn't have any diagrams illustrating what
> > you were describing.
>
> What diagrams would you suggest to enhance the explanation?
Well, for example, a diagram illustrating what you meant by a 3x3
square... where is the knight in relation to that square? It's not
clear from your explanation. I happen to know exactly what you meant,
because there's a similar rule in Alexander's Technique, and because I
evaluated and tried out several knight positions relative to a 3x3
square on the board.. but if you had a simple diagram, it would have
been much easier to see what you meant.
That's just one example. There are others, such as diagrams
illustrating the starting and ending squares of the knight, in addition
to the path it would take to get between those squares. This would be
especially useful in longer knight paths.
And there are other still. But I'm not here to give you specific advice
on writing your own book, but simply to make the point that diagrams can
make an explanation clearer.
> > I would rather have something clearly explained in more pages than a
> > optimally condensed, but less than optimally clear explanation.
>
> So would I. But what part of my explanation was causing difficulties
> for you? Perhaps I can explain that part better.
See above.
> > You are really grasping at straws. At first you were harping that
> > it took a whole 80 pages to explain the method. Now that I've
> > pointed out that it only takes 8 pages you're still not satisfied,
> > as you can explain your own method in only one page.
>
> If I did claim that it took all eighty pages after you'd already said
> that only eight pages gave the method, I apologise for the inaccuracy
> and any confusion that may have caused. As I recall, I merely
> complained that I didn't see the need for an eighty-page book on the
> topic and, really, it doesn't matter what the other seventy-two pages
> contain.
Yes. You don't need an 80 page book. But that's quite irrelevant to
the point at hand, considering that you don't even need to read the
full 80 pages of the "Knight Moves" book to learn Alexander's
Technique. As I said, 40 pages are about why the technique works the
way it does, 8 pages for learning the method, and the rest of the book
are examples, exercises, answers, reference, and index... Sure, those
might also be superfluous (strictly speaking... if you want just the
bare bones description of the method and nothing more), but I think they
add to the value of the book.
> > So, if a method can't be explained in one page it's not worth
> > learning? How many one-page chess books have you bought recently?
>
> If a method can't be explained in one page but an alternative method
> of doing exactly the same thing can be explained in one page, I know
> which one I'll go for.
But your method doesn't do the same thing, since is error prone,
potentially slow and confusing (for longer paths).
But, even if the methods were identical, just because each method
could be explained in one page (as could Alexander's Technique, if you
took out the diagrams and tried to cram in as much text as possible on
to a single page) doesn't mean that that's the best way of explaining
the method.
Clarity and ease of learning the method also count for something. I'd
pick the clearest and easiest to learn explanation rather than the
shortest one.. especially as we're talking only about 15 minutes of
reading time, for the longer explanation, if that. It's really
splitting hairs to insist the method must be explained on one page in
this case.
> >> Alexander's technique sounds to me like a very hard way to do
> >> something nearly trivial.
> >
> > Is your own rule of "Moving to the opposite corner of a 3x3 square
> > always takes four moves" a "very hard way to do something nearly
> > trivial"? Because Alexander's Technique consists of rules no harder
> > than that.
>
> No, it's a trivial way to do something nearly trivial. How many such
> rules does Alexander's Technique actually have? You've not actually
> said, as I recall, other than that it takes eight pages to list them.
I haven't counted them, but there are one or two rules per length of
the minimum knight path we're talking about (ie. 1 through 6)... so
maybe between 8 and 12 rules. Not really much (if at all) longer than
your own method.
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Date: 13 Oct 2007 13:12:44
From: David Richerby
Subject: Re: Counting knight moves
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foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> foot <[email protected]> wrote:
>>> Not to mention that you didn't have any diagrams illustrating what
>>> you were describing.
>>
>> What diagrams would you suggest to enhance the explanation?
>
> Well, for example, a diagram illustrating what you meant by a 3x3
> square... where is the knight in relation to that square? It's not
> clear from your explanation.
Nice troll. You had me.
Dave.
--
David Richerby Old-Fashioned Portable Tool (TM):
www.chiark.greenend.org.uk/~davidr/ it's like a handy household tool but
you can take it anywhere and it's
perfect for your grandparents!
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Date: 12 Oct 2007 21:53:03
From: foot
Subject: Re: Counting knight moves
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On 12 Oct 2007 15:52:03 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> I note that it's offside for me to call AT `fancy' but just fine
> >> for you to call my technique `much vaunted'.
> >
> > You are vaunting about your technique... constantly. So to call it
> > "much vaunted" is simply to state a fact.
>
> I've promoted it no more than you've promoted Alexander's. I've
> presented it as a simple way of doing something that isn't difficult;
> you've presented Alexander's technique as some great discovery that
> will be of practical benefit to most chess players. It sounds to me
> that your use of the phrase `much vaunted' serves no function except
> to be a hypocritical perjorative.
No, it's a simple statement of fact. You vaunted your method quite a
lot, and I just called your method by what it was: a much vaunted
method. Whether the method I reviewed was also much vaunted or not is
really beside the point, as I never claimed that a method must be bad
if it was much vaunted. It would indeed be hypocritical if I did claim
that, but I never did.
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Date: 12 Oct 2007 21:50:41
From: foot
Subject: Re: Counting knight moves
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On Fri, 12 Oct 2007 16:51:14 -0000 SBD <[email protected] > wrote:
>
> On Oct 12, 9:04 am, foot <[email protected]> wrote:
>
> >
> > It's very constructive criticism on your part to call the method
> > taught in the book a "parlor trick". We're all very grateful for
> > your insight. You know, when I hear constructive criticism of that
> > caliber, my heart swells with pride at the wonder that is USENET.
>
> Can you show it is any more than that? Or will we again enter the
> circular argument of "giving it away"?
It's not a circular argument that revealing the method gives it away.
That's what giving the method away means: revealing it. This is a
simple statement of fact. The argument is that I don't want to reveal
the method because I feel it would be unfair to the author, who
deserves to be rewarded for his work.
If you wish for the method to be revealed without reading the book, I
suggest you talk to the author, not to me... because I'm not doing it.
> If you cannot even show one example of its supposed superiority,
> why should we bother?
I gave you the reasons why and I gave you examples of situations where
it would be useful. Now, as to **proving** that the method actually
does work without error and as quickly as I claimed requires actually
using the method, and using the method requires learning the method.
And you can't learn the method unless either A - I reveal the method
(which I'm not going to do), or B - you get the book yourself (which
you evidently aren't going to do).
> All you keep doing is insisting that this method is "better" and
> you don't even know what it is better than - except that,
> supposedly, without it, all is "trial and error."
What?
Have you actually followed this conversation? I was talking about the
"ordinary" method of counting knight moves (which is just to try making
some moves until you get to your destination square), and the method Mr
Richerby outlined (which involves some of the same, along with a few of
his own rules). That's what Alexander's Technique is better than.
> > > If the method can be given away that easily, it is
> > > not worth paying for.
> >
> > Right. It's impossible for simple, useful methods to be worth
> > anything. They all have to be complex, unwieldy, and hard to teach.
> > Only then do you know you're getting your money's worth.
>
> I prefer not to spend anything at all on a dubious method for doing
> something that is already simple to do.
Simple. Error prone. And slow.
While Alexander's Technique is also simple, but not nearly as error
prone, and it's faster.
> You continue to claim that we wallow in some pool of complexity;
> that assumption is flawed.
Well, you might not... perhaps the shortest path that a knight could
take to a given square is as obvious as a one-move knight move to you
(in which case you've got some extraordinary ability far superior
to your average chess player). But, if not, and you use the "ordinary"
trial and error method of counting knight moves then you are wallowing
in needless complexity because the technique taught in this book is
more simpler, faster, and more reliable.
And I'm starting to get really sick of repeating myself here and of all
this endless bickering.
When I reviewed the book I didn't intend to start a 100 message flame
war. I think I've said all I can say here without continuing to repeat
myself, and I also think we understand each other at this point, and
aren't going to convince each other either way. So further discussion
of this is pretty useless.
So I'm going to reply to all the outstanding messages in this thread at
this moment and call it a day. You guys can continue arguing with each
other, or agreeing with each other, or whatever... I'm bored of it,
and, frankly, have much better things to do than repeat myself on this
issue.
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Date: 12 Oct 2007 20:44:19
From: foot
Subject: Re: Counting knight moves
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On 12 Oct 2007 14:09:22 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> I assure you that I'm just an ordinary player. I have no especial
> >> skill at the game.
> >
> > I think you do. You've already demonstrated that you know more than
> > most chess players by the rules you've set out in your own
> > technique,
>
> Correction: I have already demonstrated that I know more than you
> believe most chess players know.
Do you really think most chess players know the method you describe?
Or really anything more than to just use trial and error to move their
knight around (in their head) when looking to find the minimum
number of moves it takes to get to a given square? I don't. I really
doubt they even know your 3x3 rule, or that it always takes an even
number of moves to get to a same-colored square.
> > Conversely, though you yourself don't seem to mind using some rules
> > such as this (the ones you already know), you object to learning
> > more such rules. If you were consistent, you'd denounce your 3x3
> > rule and all the rest of the time-saving rules you know and insist
> > on using pure trial and error knight moves.
>
> That doesn't follow at all. I have proposed a small set of
> special-case rules plus a (chess-based) technique for getting to a
> place where those rules can be applied. You are advocating a much
> larger set of rules.
So first you were objecting to the fact that Alexander's Technique used
rules at all instead of trial and error mucking about with the knight,
until I pointed out that your own method also used rules. And now you
object to there being too many of these rules?
This is quite similar to what you did earlier when you objected to
having to read 80 whole pages to learn the method, but when I pointed
out that you'd only need to read 8 pages, that suddenly wasn't good
enough for you either.
You're obviously never going to be satisfied, and are determined to
reject the method no matter what its real merits are.
But, back to your new objection about Alexander's Technique consisting
of "a much larger set of rules". You don't even know the method, or how
many rules it has, so how can you make pronouncements about there
being a "much larger set" of them?
And even if Alexander's Technique has more rules than your method, does
that necessarily mean the method is not worth learning? Chess is not
a simple game. How many hundreds of rules do chess players eagerly
learn in order to play the game well at all? Could the learning of
rules, when they make your task easier, faster, and more reliable be
worth it? I think so, when the alternative is a slow, unreliable trial
and error method that might lead to confusion over the board.
> My position is that a large number of those rules are redundant
> because their effects can be obtained from simple chess calculation.
The classic rule of the square endgame method is also "redundant" in
that the results you get from applying it can be obtained from simple
chess calculation. Yet it's considered a basic endgame technique which
I doubt you'd have much luck getting players to abandon.
> > And yet you embrace such rules on the one hand (apparently, when
> > you've come up with them yourself or got them from some other
> > source), but object to them when they come from this book.
>
> My objection to the technique is emphatically not that I didn't invent
> it or find out about it before you did.
So you claim. But that seems to be the only explanation consistent
with the facts.
> >>> Well, the trial and error parts of the method you describe is
> >>> [...] more like trying to solve a maze by randomly picking
> >>> directions, instead of always making right hand turns.
> >>
> >> No, for two reasons. Firstly, I'm not advocating moving randomly.
> >> Secondly, the moving the knight close to the right direction and
> >> then correcting at the end always works.
> >
> > "Moving in the direction of your goal" in a maze is not a very
> > good strategy.
>
> That's exactly what I wrote in my next sentence:
>
> >> Trying to move in the right direction in a maze might send you
> >> completely the wrong way.
Ooops. Since I had mentioned the strategy of always making right hand
turn, I misread what you said as "trying to [always] move right in
a maze might send you completely the wrong way". My mistake. We
actually seem to be in agreement here.
> But knights don't move in a maze.
Actually, it is quite analogous to a maze, where (imagining) moving the
knight by trial and error can get you "lost", or at least send you
temporarily down the wrong path. The whole point of Alexander's
Technique is to try to improve upon this inefficient and error prone
method of counting knight moves.
> OK, perhaps my method isn't strictly faster but I doubt that it would
> be any slower. Besides, my method is fast enough that it is far from
> being the weakest point of my chess playing. I'd benefit much more
> from spending an afternoon working on my tactics or studying a couple
> of master games than I would from learning this method.
Well, as I said, whether you learn this method or not is none of my
concern. It's no skin off my back either way. However, I do hope that
other people will decide whether a method like this can be useful for
themselves.
> > Also, I would question whether your method gets the correct answer
> > each time, as it seems to involve trial and error and guessing.
>
> It's not let me down yet... I've already explained that it's
> practically impossible to guess wrong but you just jump up and down on
> this word `guess' as if it necessarily implies inaccuracy.
It implies the possibility of inaccuracy... a much great possibility of
inaccuracy than Alexander's Technique, anyway.
--Sergey
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Date: 12 Oct 2007 16:51:14
From: SBD
Subject: Re: Counting knight moves
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On Oct 12, 9:04 am, foot <[email protected] > wrote:
>
> It's very constructive criticism on your part to call the method taught
> in the book a "parlor trick". We're all very grateful for your
> insight. You know, when I hear constructive criticism of that caliber,
> my heart swells with pride at the wonder that is USENET.
Can you show it is any more than that? Or will we again enter the
circular argument of "giving it away"? If you cannot even show one
example of its supposed superiority, why should we bother? All you
keep doing is insisting that this method is "better" and you don't
even know what it is better than - except that, supposedly, without
it, all is "trial and error."
>
> > If the method can be given away that easily, it is
> > not worth paying for.
>
> Right. It's impossible for simple, useful methods to be worth
> anything. They all have to be complex, unwieldy, and hard to teach.
> Only then do you know you're getting your money's worth.
I prefer not to spend anything at all on a dubious method for doing
something that is already simple to do. You continue to claim that we
wallow in some pool of complexity; that assumption is flawed.
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Date: 12 Oct 2007 10:04:21
From: foot
Subject: Re: Counting knight moves
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On Fri, 12 Oct 2007 13:15:21 -0000
SBD <[email protected] > wrote:
>
> On Oct 12, 7:50 am, David Richerby <[email protected]>
> wrote:
>
> > I note that it's offside for me to call AT `fancy' but just fine for
> > you to call my technique `much vaunted'.
>
> It has been a rather odd debate from his side. He reminds me of the
> colleagues I had who would send proposals and such your way for review
> and print, in big letters, CONSTRUCTIVE criticism requested. It meant
> they wanted no criticism at all! In fact, trying to help them was the
> biggest mistake you could make - it got so that later in my academic
> career I just sent such things back with some triviality like "Good
> idea!" attached - it was not even worth reading. If you wanted them to
> think you really read it you just thought up some other nice comment
> to include in the middle as well as noting 2-3 spelling errors.....
Cute anecdote.
> He called for discussion, but then felt compelled simply to attack
> anything you noted, instead of thinking, "hey, maybe the method does
> suck after all!" or trying to boost its value with salient examples
> (beyond the most simplistic tripe).
>
> At this point I would simply consider him a shill for the book. Things
> like "hard work that went into the book" and "giving it away" are
> laughable- at best it is a parlor trick on the level of "Hey! I found
> a quarter behind your ear!" - and thus, not even worth the discussion
> he claimed to want.
It's very constructive criticism on your part to call the method taught
in the book a "parlor trick". We're all very grateful for your
insight. You know, when I hear constructive criticism of that caliber,
my heart swells with pride at the wonder that is USENET.
> If the method can be given away that easily, it is
> not worth paying for.
Right. It's impossible for simple, useful methods to be worth
anything. They all have to be complex, unwieldy, and hard to teach.
Only then do you know you're getting your money's worth.
> And of course, being chained to a method rather than understanding why
> the method works - and thus, moving beyond it - keeps his discourse
> (and probably playing ability) very limited.
"Understanding why the method works"? Just how has anyone here offered
any insight in to that at all? You don't even know the method, much
less know why it works. In fact, half the book is an explanation of
why it work... so I really don't know what you're getting at here.
And as for "moving beyond" the method, that's a joke, coming from
people who insist on sticking with trial and error jumping around that
they've used since childhood. Where's your willingness to "move beyond"
that method?
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Date: 12 Oct 2007 09:54:12
From: foot
Subject: Re: Counting knight moves
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On 12 Oct 2007 13:50:07 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> While the knight can, of course, never get to the target square in
> less than the minimum number of moves (say five), if the knight can
> cause sufficient threats on the way (or give check), it might still be
> able to get there before the opponent makes five moves towards his
> goal (such as promoting a given pawn).
>
> I wouldn't press the point strongly but, in a way, the knight can
> cross the board in `less than' the minimum number of moves.
In certain circumstances, yes. And then it's up to the player to
figure out if those circumstances apply to the position on the board.
But if, say, your king is not anywhere near the path of your opponent's
knight, he's not going to be able to give check to your king on the way
to the queening pawn.
In fact, in my own endgames where knights have tried to stop pawns from
queening, it's pretty rare that these knights manage to get to the
pawns "faster" by giving check along the way. Of course, your mileage
may vary... and, as I said, don't expect the method to do all the work
for you in every conceivable situation. But, overall, when knights are
involved in a series of moves it's useful.
> > Besides, even if Alexander's Technique was useless, your own much
> > vaunted alternative method would be just as useless, since it does
> > no more (and, I'd argue, quite a bit less) than Alexander's
> > Technique does.
>
> I note that it's offside for me to call AT `fancy' but just fine for
> you to call my technique `much vaunted'.
You are vaunting about your technique... constantly. So to call it
"much vaunted" is simply to state a fact. Whereas I don't even know
where you got the idea that Alexander's Technique was "fancy" in any
way. What does it even mean for a technique to be "fancy"? Sounds
like it serves no function except to be a pejorative.
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Date: 12 Oct 2007 15:52:03
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> I note that it's offside for me to call AT `fancy' but just fine for
>> you to call my technique `much vaunted'.
>
> You are vaunting about your technique... constantly. So to call it
> "much vaunted" is simply to state a fact.
I've promoted it no more than you've promoted Alexander's. I've
presented it as a simple way of doing something that isn't difficult;
you've presented Alexander's technique as some great discovery that
will be of practical benefit to most chess players. It sounds to me
that your use of the phrase `much vaunted' serves no function except
to be a hypocritical perjorative.
Dave.
--
David Richerby Crystal Dangerous T-Shirt (TM):
www.chiark.greenend.org.uk/~davidr/ it's like a fashion statement but it
could explode at any minute and it's
completely transparent!
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Date: 12 Oct 2007 13:19:40
From: SBD
Subject: Re: Counting knight moves
|
On Oct 12, 8:09 am, David Richerby <[email protected] >
wrote:
> Correction: I have already demonstrated that I know more than you
> believe most chess players know.
A good point. Too many chess books are already "written down" for a
mass audience of idiots. Every so often some unknown pops up with such
a book - "Chess Puzzles for the Causal Player!" and other such rot,
trying to claim you'll be able to beat the local 500 Elo with a
minimum of work. Find an old Reinfeld pdf on the web for free, and
you'll learn more in an hour by going over classic games and puzzles
than you would from 40 hours of study of tripe like that.
These books for "average" or "casual" players are often written by
folks who have no business trying to teach you chess.
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Date: 12 Oct 2007 13:15:21
From: SBD
Subject: Re: Counting knight moves
|
On Oct 12, 7:50 am, David Richerby <[email protected] >
wrote:
> I note that it's offside for me to call AT `fancy' but just fine for
> you to call my technique `much vaunted'.
It has been a rather odd debate from his side. He reminds me of the
colleagues I had who would send proposals and such your way for review
and print, in big letters, CONSTRUCTIVE criticism requested. It meant
they wanted no criticism at all! In fact, trying to help them was the
biggest mistake you could make - it got so that later in my academic
career I just sent such things back with some triviality like "Good
idea!" attached - it was not even worth reading. If you wanted them to
think you really read it you just thought up some other nice comment
to include in the middle as well as noting 2-3 spelling errors.....
He called for discussion, but then felt compelled simply to attack
anything you noted, instead of thinking, "hey, maybe the method does
suck after all!" or trying to boost its value with salient examples
(beyond the most simplistic tripe).
And of course, being chained to a method rather than understanding why
the method works - and thus, moving beyond it - keeps his discourse
(and probably playing ability) very limited.
At this point I would simply consider him a shill for the book. Things
like "hard work that went into the book" and "giving it away" are
laughable- at best it is a parlor trick on the level of "Hey! I found
a quarter behind your ear!" - and thus, not even worth the discussion
he claimed to want. If the method can be given away that easily, it is
not worth paying for.
|
| |
Date: 11 Oct 2007 16:30:30
From: foot
Subject: Re: Counting knight moves
|
On Thu, 11 Oct 2007 13:33:15 -0000 SBD <[email protected] > wrote:
>
> I think the reason this can't be discussed intelligently is that we
> really need to see some of these wonderful examples (using the
> language of chess, not words) in the book, but if they turn out to be
> nonsense, we''ll just feel cheated on the price of the book...... and
> evidently Alexander has no free samples to give, say from a web site??
Well, the examples in the book are just examples of how the method is
applied (ie. a starting and destination square are shown, and then the
method is followed, step by step, until the answer is arrived at).
They're not examples designed to illustrate the kinds of **positions**
where wanting to find out the minimum number of moves a knight would
take to get from one square to another would be useful. In other
words, no other pieces or pawns are shown to be on the board. And
you're not told (or are expected to infer) why moving to that square
might be desirable. That's all up to the player to figure out by other
means.
So, while I'm sure it would be nice to see the examples of the method
in action given in the book, that would give away the method itself,
and would make buying the book (to a certain extent) superfluous...
which is something that I feel would be unfair to the author,
considering all the hard work he obviously put in to figuring out and
publishing the method in the first place.
|
| |
Date: 11 Oct 2007 14:33:15
From: foot
Subject: Re: Counting knight moves
|
On 11 Oct 2007 15:21:47 +0100 (BST)
David Richerby <[email protected] > wrote:
> SBD <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> Secondly, the moving the knight close to the right direction and
> >> then correcting at the end always works. Trying to move in the
> >> right direction in a maze might send you completely the wrong way.
> >
> > Could you give an example of this, because in many chess problems
> > that is precisely the problem: you think you are going the correct
> > route with the knight but realize you had to "lose a move" or "move
> > back then forward".
>
> Alexander's Technique only tells you the answer to the question `What
> is the minimum number of moves required to get a knight from A to B on
> a completely empty chess board.' My replacement technique has the
> same goals. In real life (or even in a puzzle ;-) ) the opponent's
> moves and the placement of the other pieces on the board interfere.
Whether or not other pieces interfere, the knight in question is never
going to take less than the minimum number of moves, given by
Alexander's Technique, to reach a square. Thus, the method can still
be useful in situations where there are other pieces on the board.
Of course, the method won't magically do everything for you. So it's up
to the other tools has in their toolbox to figure out whether the
knight in question will, in fact, reach the destination square in the
minimum number of moves, what moves the shortest path consists of,
etc...
But just because the method won't do everything, or can't be used in
every conceivable situation, doesn't mean it's useless in real games
(even when other pieces are involved). As I stated in my earlier
example, just because there are other pieces on the board doesn't mean
that they'll be able to (or will) interfere with the knight going to
its destination square. And even if they could, that might be quite
irrelevant if you've already figured out that even the minimum number
of moves are too many moves to achieve what the knight needs to do
(say, stop a pawn from queening).
Besides, even if Alexander's Technique was useless, your own much
vaunted alternative method would be just as useless, since it does no
more (and, I'd argue, quite a bit less) than Alexander's Technique does.
|
| | |
Date: 12 Oct 2007 13:50:07
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Alexander's Technique only tells you the answer to the question
>> `What is the minimum number of moves required to get a knight from
>> A to B on a completely empty chess board.' [...]
>
> Whether or not other pieces interfere, the knight in question is
> never going to take less than the minimum number of moves, given by
> Alexander's Technique, to reach a square. Thus, the method can
> still be useful in situations where there are other pieces on the
> board.
While the knight can, of course, never get to the target square in
less than the minimum number of moves (say five), if the knight can
cause sufficient threats on the way (or give check), it might still be
able to get there before the opponent makes five moves towards his
goal (such as promoting a given pawn).
I wouldn't press the point strongly but, in a way, the knight can
cross the board in `less than' the minimum number of moves.
> Besides, even if Alexander's Technique was useless, your own much
> vaunted alternative method would be just as useless, since it does
> no more (and, I'd argue, quite a bit less) than Alexander's
> Technique does.
I note that it's offside for me to call AT `fancy' but just fine for
you to call my technique `much vaunted'.
Dave.
--
David Richerby Impossible Peanut (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ roasted nut but it can't exist!
|
| |
Date: 11 Oct 2007 14:21:22
From: foot
Subject: Re: Counting knight moves
|
On 11 Oct 2007 11:35:50 +0100 (BST)
David Richerby <[email protected] > wrote:
> SBD <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> Alexander's technique sounds to me like a very hard way to do
> >> something nearly trivial.
> >
> > Perhaps, but following the conversation, I began to wonder if it
> > might have value for things like composing long seriesmovers with
> > one or more knights. And there is an American author who recommends
> > modified seriesmovers (Albertston, Chess Mazes) for developing
> > tactical vision.
>
> It might be useful for that, yes. The only other suggestion was for
> knight endgames but
That wasn't the only other suggestion. This method is also useful in
middlegames, where (for example) you need to move your knight from,
say, the queenside to the kingside. If you use the technique to figure
out that you need 5 moves to get the knight to its destination square,
but you only have 4 moves in which to do it, you could abandon the
attempt and concentrate on finding another solution.
It also has the potential to be useful where two knights are racing to
reach the same square... or, pretty much any time counting more than a
couple of knight moves becomes important.
> there, the whole point is that the enemy king can move.
The king may be able to move, but that doesn't mean he's going to be
able to stop the knight. Same with any other piece on the board.
Of course, the method taught in the book won't tell you if the any other
piece is going to affect a knight, but it will tell you what the
minimum number of moves getting to a particular square will take. And
I still think that can be quite useful... especially when the
alternative is an error prone and time consuming trial and error method.
|
| |
Date: 11 Oct 2007 12:34:53
From: foot
Subject: Re: Counting knight moves
|
On 11 Oct 2007 10:46:55 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> > As I've said several times now, the part of the book that teaches
> > the method only takes up 8 pages!
>
> This is obviously some strange new meaning of the word `only' of which
> I was previously unaware. Mine took less than half a page.
Yes. And yours isn't even half as useful. Not to mention that you
didn't have any diagrams illustrating what you were describing. I
would rather have something clearly explained in more pages than a
optimally condensed, but less than optimally clear explanation.
You are really grasping at straws. At first you were harping that
it took a whole 80 pages to explain the method. Now that I've pointed
out that it only takes 8 pages you're still not satisfied, as you can
explain your own method in only one page.
So, if a method can't be explained in one page it's not worth
learning? How many one-page chess books have you bought recently?
This is really getting ridiculous. You're obviously never going to be
satisfied no matter what I say.
Stick to your method. Enjoy it. No one's forcing you to learn
anything.
But hopefully other players will understand how useful the method
taught in the book can be, and will find it worth their while.
> Alexander's technique sounds to me like a very hard way to do
> something nearly trivial.
Is your own rule of "Moving to the opposite corner of a 3x3 square
always takes four moves" a "very hard way to do something nearly
trivial"? Because Alexander's Technique consists of rules no harder
than that.
|
| | |
Date: 12 Oct 2007 14:18:33
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> foot <[email protected]> wrote:
>>> As I've said several times now, the part of the book that teaches
>>> the method only takes up 8 pages!
>>
>> This is obviously some strange new meaning of the word `only' of
>> which I was previously unaware. Mine took less than half a page.
>
> Yes. And yours isn't even half as useful.
In what way? It does exactly the same thing.
> Not to mention that you didn't have any diagrams illustrating what
> you were describing.
What diagrams would you suggest to enhance the explanation?
> I would rather have something clearly explained in more pages than a
> optimally condensed, but less than optimally clear explanation.
So would I. But what part of my explanation was causing difficulties
for you? Perhaps I can explain that part better.
> You are really grasping at straws. At first you were harping that
> it took a whole 80 pages to explain the method. Now that I've
> pointed out that it only takes 8 pages you're still not satisfied,
> as you can explain your own method in only one page.
If I did claim that it took all eighty pages after you'd already said
that only eight pages gave the method, I apologise for the inaccuracy
and any confusion that may have caused. As I recall, I merely
complained that I didn't see the need for an eighty-page book on the
topic and, really, it doesn't matter what the other seventy-two pages
contain.
> So, if a method can't be explained in one page it's not worth
> learning? How many one-page chess books have you bought recently?
If a method can't be explained in one page but an alternative method
of doing exactly the same thing can be explained in one page, I know
which one I'll go for.
>> Alexander's technique sounds to me like a very hard way to do
>> something nearly trivial.
>
> Is your own rule of "Moving to the opposite corner of a 3x3 square
> always takes four moves" a "very hard way to do something nearly
> trivial"? Because Alexander's Technique consists of rules no harder
> than that.
No, it's a trivial way to do something nearly trivial. How many such
rules does Alexander's Technique actually have? You've not actually
said, as I recall, other than that it takes eight pages to list them.
Dave.
--
David Richerby Miniature Widget (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ thingy but you can hold in it your
hand!
|
| |
Date: 11 Oct 2007 12:24:01
From: foot
Subject: Re: Counting knight moves
|
On 11 Oct 2007 13:58:49 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> >
> > Why do you object to niche chess books? If they achieve what they
> > set out to do, what's the problem?
>
> I object to this book because any reasonable player can already
> calculate quickly and accurately the number of moves it would take a
> knight to get between two squares.
Well, this is a significant point of disagreement between us.
I don't think most chess players can do that quickly or accurately.
> Any weaker player would be better
> served by improving their board vision until they can calculate this
> using their chess skill, rather than learning the technique.
>
> >> But it's still an eighty page book and it's still eight pages to
> >> describe how to do something trivial.
> >
> > I don't think it's trivial. Nor do I think most chess players would
> > find it trivial.
>
> I assure you that I'm just an ordinary player. I have no especial
> skill at the game.
I think you do. You've already demonstrated that you know more than
most chess players by the rules you've set out in your own technique,
such as "it takes three moves to get a knight to a
horizontally/vertically adjacent square and four moves to get to the
opposite corner of a 3x3 square". I bet if I asked a random chess
player, or even a large number of random players, they wouldn't know
this rule.
Conversely, though you yourself don't seem to mind using some rules
such as this (the ones you already know), you object to learning more
such rules. If you were consistent, you'd denounce your 3x3 rule and
all the rest of the time-saving rules you know and insist on using pure
trial and error knight moves.
And yet you embrace such rules on the one hand (apparently, when you've
come up with them yourself or got them from some other source), but
object to them when they come from this book.
> > Well, the trial and error parts of the method you describe is not
> > like "walking up the stairs", but more like trying to solve a maze
> > by randomly picking directions, instead of always making right hand
> > turns.
>
> No, for two reasons. Firstly, I'm not advocating moving randomly.
> Secondly, the moving the knight close to the right direction and then
> correcting at the end always works.
"Moving in the direction of your goal" in a maze is not a very
good strategy.
> Trying to move in the right direction in a maze might send you
> completely the wrong way.
I guess you haven't solved many mazes, because if you had you'd know
that in an ordinary maze this strategy (always making right-hand turns)
is guaranteed to get you out, while choosing random directions to go in
or "moving in the direction of your goal" can keep you lost in the maze
forever (given a large enough maze).
> > But, hey, it works for you... and you seem to be in no hurry to
> > improve on it.
>
> I'm in no hurry to improve because I can already get the correct
> answer faster than I could using the technique and at least as
> accurately. The technique just isn't an improvement.
Well, considering that you neither know nor have ever tried the
technique, I don't think you're any position to claim that your method
gets the correct answer faster. Also, I would question whether your
method gets the correct answer each time, as it seems to involve
trial and error and guessing.
But, be that as a it may, whether you learn Alexander's Technique or
stick with your own method is none of my concern. My main points are
that the technique works, and would be useful to most players.
|
| | |
Date: 12 Oct 2007 14:09:22
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> I assure you that I'm just an ordinary player. I have no especial
>> skill at the game.
>
> I think you do. You've already demonstrated that you know more than
> most chess players by the rules you've set out in your own
> technique,
Correction: I have already demonstrated that I know more than you
believe most chess players know.
> Conversely, though you yourself don't seem to mind using some rules
> such as this (the ones you already know), you object to learning
> more such rules. If you were consistent, you'd denounce your 3x3
> rule and all the rest of the time-saving rules you know and insist
> on using pure trial and error knight moves.
That doesn't follow at all. I have proposed a small set of
special-case rules plus a (chess-based) technique for getting to a
place where those rules can be applied. You are advocating a much
larger set of rules. My position is that a large number of those
rules are redundant because their effects can be obtained from simple
chess calculation.
> And yet you embrace such rules on the one hand (apparently, when
> you've come up with them yourself or got them from some other
> source), but object to them when they come from this book.
My objection to the technique is emphatically not that I didn't invent
it or find out about it before you did.
>>> Well, the trial and error parts of the method you describe is
>>> [...] more like trying to solve a maze by randomly picking
>>> directions, instead of always making right hand turns.
>>
>> No, for two reasons. Firstly, I'm not advocating moving randomly.
>> Secondly, the moving the knight close to the right direction and then
>> correcting at the end always works.
>
> "Moving in the direction of your goal" in a maze is not a very
> good strategy.
That's exactly what I wrote in my next sentence:
>> Trying to move in the right direction in a maze might send you
>> completely the wrong way.
>
> I guess you haven't solved many mazes, because if you had you'd know
> that in an ordinary maze this strategy (always making right-hand turns)
> is guaranteed to get you out, while choosing random directions to go in
> or "moving in the direction of your goal" can keep you lost in the maze
> forever (given a large enough maze).
That's exactly what I meant by `might send you completely the wrong
way'! I was trying to move towards the goal in a maze is a bad
strategy. (By the way, always turning in the same direction only
works if the maze is connected, which most traditional hedge mazes
are.)
But knights don't move in a maze. They move on a chess board, in a
very regular way and, specifically, in a way that means that heading
towards the goal until you get close to it will always work.
>>> But, hey, it works for you... and you seem to be in no hurry to
>>> improve on it.
>>
>> I'm in no hurry to improve because I can already get the correct
>> answer faster than I could using the technique and at least as
>> accurately. The technique just isn't an improvement.
>
> Well, considering that you neither know nor have ever tried the
> technique, I don't think you're any position to claim that your
> method gets the correct answer faster.
OK, perhaps my method isn't strictly faster but I doubt that it would
be any slower. Besides, my method is fast enough that it is far from
being the weakest point of my chess playing. I'd benefit much more
from spending an afternoon working on my tactics or studying a couple
of master games than I would from learning this method.
> Also, I would question whether your method gets the correct answer
> each time, as it seems to involve trial and error and guessing.
It's not let me down yet... I've already explained that it's
practically impossible to guess wrong but you just jump up and down on
this word `guess' as if it necessarily implies inaccuracy.
Dave.
--
David Richerby Radioactive Lotion (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ soothing hand lotion but it'll make
you glow in the dark!
|
| |
Date: 11 Oct 2007 11:58:59
From: foot
Subject: Re: Counting knight moves
|
On 11 Oct 2007 13:45:46 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> Again, I had no problems whatsoever getting a knight from g1 to a6
> >> in five moves and convincing myself that three is impossible.
> >> Heading straight for a6 puts you on c3/d4/e5 after two moves and
> >> a4/b5/c6/d7 after three. All of those squares are two moves from
> >> a6; if you can't instantly see that they are, you really need to
> >> work on your visualization.
> >
> > If you asked me whether a4 was a minimum of three moves away, I
> > couldn't instantly tell you whether it was or not without using
> > Alexander's Technique.
>
> I'm pretty sure you said that Alexander's Technique was taking you ten
> to fifteen seconds. That's not instant.
Here is what I said:
"It only took me a few minutes to start applying the rules after I'd
read the book, and maybe another ten minutes to half an hour to
completely internalize them... and after an hour or so of practice, I
feel completely confident I'd be able to quickly (certainly under
about 15 seconds, and often as little as a second or two)"
How long the calculation takes depends on which destinations
square(s) I'm interested in. 15 seconds was the maximum it took me to
figure out the minimum number of moves to a given square. Often, it
took much less. Sometimes as little as a second.
And the 15 seconds is probably a conservative estimate. I didn't
really time myself, so I was just going by what I felt was the time it
took to calculate the answer. So even the longest calculation might
have taken significantly less time... But I didn't want to promise more
than the method could deliver, so I erred on the longer side.
Furthermore, this right after I first learned the technique and
practiced it for only about an hour. I'm sure with further practice it
will probably take me much less time.
> Now, I couldn't tell you *instantly* but after making the attempt
> g1-e2-b3-a4, it should be obvious that you can't get any closer than
> that in three moves. That wouldn't have taken me more than a couple
> of seconds.
A very error-prone method, as you just demonstrated yourself: the
knight can't even move from b3 to a4.
> >> (I'm not claiming that I computed all of that in my head to work
> >> out the move-count. I just mean that the squares I gave are the
> >> places you could get to from your interpretation of `start at g1
> >> and head straight for a6.)
> >
> > Well, let's say you did head "straight for a6" from g1... and you
> > went to f3-d4-b5 and now where?
>
> b5 and a6 are diagonally adjacent! b5-c7-a6. If you can't see the
> two-move path between diagonally adjacent squares, I can understand
> why you're reluctant to use my trial-and-error method.
But not every diagonally adjacent square is two moves away. Even you,
who are so adamant about using your trial and error method, have to
take that fact in to account.
> I assure you that I'm not a gifted chess player -- I'm doing
> absolutely nothing special.
No, I think the parts of your method that don't consist of trial and
error moving of the knight around are something special. Indeed, those
special rules are very similar to what's in the book (though the book
has more). And most ordinary chess players are not aware of these rules.
> It seems to me that you have very poor board vision. Are you a new
> player?
I'd rather stick to discussing the technique than starting to talk
about me.
> >> But the technique involves applying eight pages of rules that have
> >> nothing to do with chess per se.
> >
> > What does it matter whether the rules "have to do with chess per se"
> > (a point that could be debated.. but I don't want to go there) ? As
> > long as it works, works quickly, and eliminates the possibility of
> > error and confusion?
>
> The advantage of chess-based reasoning is that it help your
> understanding of other parts of the game and reinforces your ability
> to calculate in your head. Other rules can't be applied to anything
> else.
Well, it's not like by using Alexander's Technique you're no longer
practicing moving your knight around (in your mind). You still have to
do that to find moves make up the shortest path (when you're interested
in that information), and when you're looking to perform or prevent
some tactic. Alexander's Technique just saves you some guessing, trial
and error movement, time, and possible confusion. Well worth it, in my
opinion.
> > For example, say you have a pawn on a4 that will queen in 4 moves.
> > You opponent has a knight on g1. Will he be able to stop your pawn?
> > You apply the method and virtually immediately know that it will
> > take that knight at least 5 moves to get to a8. So you don't even
> > care what path he's going to try to get there. You can confidently
> > ch your pawn forward.
>
> But knight endgames aren't that simple! Where's his king? Can it
> stop the pawn?
Whether a king can stop a pawn is a matter of applying other endgame
techniques (such as the rule of the square). But we're talking about
knights here, not kings. Alexander's Technique never promised to solve
all your problems, but it's certainly useful for solving some.
> Can he gain a tempo by checking you with his knight on the way to a8?
> (An extremely important resource in knight endgames.)
Point well taken. You will have to take the position of the pieces in
to account to some extent, but nevertheless, as far as determining the
minimum number of moves a knight will take to get to a square goes,
this method will save you time, error, and confusion.
> If your king's on b5/c4/d5/d7/e6/e8, it's enough for him to get his
> knight to b6/c7 immediately after you promote, forking your king and
> new queen. (Another important resource) Or will you be promoting
> with check so he doesn't have time to do that?
Ok. So you've managed to find one case where using Alexander's
Technique alone won't be enough to win the game. But the no one ever
promised you will win with this technique, or that you won't have to
use other technique in addition to it. It's just another tool in a
good payer's toolbox.
It's actually good that you brought up the position of the kings, since
the rule of the square (one of the most basic and useful endgame
techniques) is also not useful without exception. It only works when
there are no pawns or pieces on the king's path to catching the
opponent's pawn.
And yet, applying your reasoning, that technique is useless! Better to
count the squares to the pawn every time, since it's easy to think up
exceptions to the rule where it just doesn't work. I would like to see
how far you get railing against people learning basic endgame
techniques such as the rule of the square.
> > I really don't see the need to use pejorative terms like "fancy" in
> > regards to something you have no knowledge of. It's really quite
> > amazing how some people will put up a tremendous amount of
> > resistance and hostility to learning anything new.
>
> I'm resistant to learning a slower, more cumbersome way to do
> something which I can already do and feel that any chess player beyond
> a beginner should be able to do.
The trial and error method that you advocate is the slower, more
cumbersome, and more error-prone way. So I would think that you'd
welcome a better way. But, you are obviously very set in your ways.
Hopefully other chess players are more open minded.
> > You know, I actually like learning new things.
>
> So do I. I'm an academic -- it's even my job to learn new things!
Hmmm
> > When there's something new to learn that gets me interested and
> > excited. I thought by mentioning that there was something new,
> > interesting and useful to learn I'd get positive reactions from this
> > group. Instead all I got was invective from people who apparently
> > can't be bothered to learn anything new. I think that's pretty sad.
>
> I don't think this technique is either interesting or useful: that's
> the point I've been making. It's not that I can't be bothered to
> learn it; I've looked at it (through your descriptions) and found it
> to be not worth the time or effort.
So you can't be bothered to learn it. Which is what I said. You just
confirmed it yourself.
> I don't even think the technique is helping you very much, either,
> since it seems that you have great difficulty using your knowledge
> that there's a five-move path between two squares to actually find
> such a path -- that's what I think you should be spending your time
> working on.
Alexander's Technique was not designed to and never promised to find
the actual path a knight must take to get somewhere in the minimum
number of moves. I don't know what gave you the idea that I had "great
difficulty" finding such a path, but even if that were the case, that's
not a shortcoming of Alexander's Technique, but a completely separate
issue.
> I'm sorry if my criticism of the technique you've been advancing came
> across as criticism of you. It probably sounded like it was but it
> wasn't intended as such.
Well, when you say things such as "It seems to me that you have very
poor board vision." That's not criticism of the technique. That's
criticism of my ability, which (apart from being wrong) is quite
irrelevant to whether the technique works or would be useful for most
chess players.
And, again, when you use pejorative terms like "fancy" to describe
something you don't even know, I think that says more about your own
attitude than about the technique.
|
| | |
Date: 12 Oct 2007 17:14:33
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> I'm pretty sure you said that Alexander's Technique was taking you
>> ten to fifteen seconds. That's not instant.
>
> Here is what I said:
>
> "It only took me a few minutes to start applying the rules after
> I'd read the book, and maybe another ten minutes to half an hour to
> completely internalize them... and after an hour or so of practice,
> I feel completely confident I'd be able to quickly (certainly under
> about 15 seconds, and often as little as a second or two)"
OK. Fifteen seconds is a long time, even as a worst case. I didn't
time my technique, either, but I can confidently say that I was
plotting paths in only two or three seconds, with confidence that I'd
done it right. Ten seconds is a long time.
>> Now, I couldn't tell you *instantly* but after making the attempt
>> g1-e2-b3-a4, it should be obvious that you can't get any closer
>> than that in three moves. That wouldn't have taken me more than a
>> couple of seconds.
>
> A very error-prone method, as you just demonstrated yourself: the
> knight can't even move from b3 to a4.
Typo, sorry. `b3' should be `c3'. Do you really think I believed
that it's legal to move a knight from e2 to b3 to a4?
>>> Well, let's say you did head "straight for a6" from g1... and you
>>> went to f3-d4-b5 and now where?
>>
>> b5 and a6 are diagonally adjacent! b5-c7-a6.
>
> But not every diagonally adjacent square is two moves away. Even
> you, who are so adamant about using your trial and error method,
> have to take that fact in to account.
Nice attempt to distract from your inability to plot a path between
the two squares. Rather than admit you'd made a mistake, you attack
me for a mistake I didn't make, thus compounding your error.
Any two diagonally adjacent squares are two moves apart, unless one or
the other is a corner, in which case they're four moves apart (as I
said upthread). Since neither b5 nor a6 is a corner, I didn't bother
to state the side condition, which is irrelevant to this case.
>> It seems to me that you have very poor board vision. Are you a new
>> player?
>
> I'd rather stick to discussing the technique than starting to talk
> about me.
I see. You're very happy to make bold assertions about what `most
chess players' do or do not know but you're not willing to state your
qualification for making such assertions.
> It's actually good that you brought up the position of the kings,
> since the rule of the square (one of the most basic and useful
> endgame techniques) is also not useful without exception. It only
> works when there are no pawns or pieces on the king's path to
> catching the opponent's pawn.
Yes but it's extremely easy to verify whether the king can reach the
queening square in time. In contrast, there don't even appear to be
any conditions which will tell you whether the answer given by
Alexander (for the totally unobstructed case) is achievable given,
say, that there is an enemy pawn on some particular square. The only
way you can check is to actually find a route.
> And yet, applying your reasoning, [the rule of the square] is
> useless! Better to count the squares to the pawn every time, since
> it's easy to think up exceptions to the rule where it just doesn't
> work. I would like to see how far you get railing against people
> learning basic endgame techniques such as the rule of the square.
Put your straw man down, please. I accept the rule of squares because
it is simple, easy to verify and demonstrably easier than plotting the
trajectories of the pieces. I reject Alexander's technique because
there are many rules, and it is hard to verify that the `theoretical'
answer is achievable without actually plotting trajectories. Using
Alexander's technique means that one has to both use the technique and
find a path; just finding a path means you only have to find a path.
>> I'm resistant to learning a slower, more cumbersome way to do
>> something which I can already do and feel that any chess player
>> beyond a beginner should be able to do.
>
> The trial and error method that you advocate is the slower, more
> cumbersome, and more error-prone way.
I disagree on all three points, as I've explained in detail on several
occasions.
>> I don't think this technique is either interesting or useful: that's
>> the point I've been making. It's not that I can't be bothered to
>> learn it; I've looked at it (through your descriptions) and found it
>> to be not worth the time or effort.
>
> So you can't be bothered to learn it. Which is what I said. You
> just confirmed it yourself.
So, you'd rather stick to discussing the technique rather than
discussing you but you're perfectly happy to discuss me. My reasons
for not learning the technique have nothing to do with laziness.
> Alexander's Technique was not designed to and never promised to find
> the actual path a knight must take to get somewhere in the minimum
> number of moves. I don't know what gave you the idea that I had
> "great difficulty" finding such a path
The following things gave me the impression that you have great
difficulty finding the path a knight must take between two squares.
1) With a knight on b5 trying to get to a6, a mere two moves away, you
asked, `now where?'
2) You said you didn't find it obvious that there is no two-move
knight path from g6 to a4.
3) You said it wasn't obvious to you that there's no path from g1 to
a6 in only three moves.
4) You spent a while challenging me to find paths of varying lengths
between squares; there would be no point challenging me to do
something you thought was easy.
> but even if that were the case, that's not a shortcoming of
> Alexander's Technique, but a completely separate issue.
Yes it is a shortcoming. Because in order to use the technique in a
game, you must be able to find the path; if you can't find the path,
what use is it to know that it's there?
>> I'm sorry if my criticism of the technique you've been advancing
>> came across as criticism of you. It probably sounded like it was
>> but it wasn't intended as such.
>
> Well, when you say things such as "It seems to me that you have very
> poor board vision." That's not criticism of the technique.
No, it's not criticism of the technique. It does, however, establish
that you are unqualified to judge the merits of the technique and
unqualified to condemn my technique as error-prone.
> That's criticism of my ability, which (apart from being wrong) is
> quite irrelevant to whether the technique works or would be useful
> for most chess players.
It is evaluation of your ability, not criticism of it. I even gave
suggestions of how to improve.
Dave.
--
David Richerby Strange Slimy Composer (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a pupil of Beethoven but it's covered
in goo and totally weird!
|
| |
Date: 11 Oct 2007 13:33:15
From: SBD
Subject: Re: Counting knight moves
|
On Oct 11, 7:58 am, David Richerby <[email protected] >
wrote:
> Secondly, the moving the knight close to the right direction and then
> correcting at the end always works. Trying to move in the right
> direction in a maze might send you completely the wrong way.
Could you give an example of this, because in many chess problems that
is precisely the problem: you think you are going the correct route
with the knight but realize you had to "lose a move" or "move back
then forward".
I suppose by correcting at the end you mean it takes maybe a move more
but it doesn't matter? Of course if it is "mate in" and you take a
move longer, it does.... I suppose if we were talking 64,000 squares
instead of 64 would the technique make more sense?
I think the reason this can't be discussed intelligently is that we
really need to see some of these wonderful examples (using the
language of chess, not words) in the book, but if they turn out to be
nonsense, we''ll just feel cheated on the price of the book...... and
evidently Alexander has no free samples to give, say from a web site??
>
> The walking up the stairs analogy wasn't intended as a direct analogy
> but just an indication that advanced techniques really aren't needed.
>
> > But, hey, it works for you... and you seem to be in no hurry to
> > improve on it.
>
> I'm in no hurry to improve because I can already get the correct
> answer faster than I could using the technique and at least as
> accurately. The technique just isn't an improvement.
>
> Dave.
>
> --
> David Richerby Accelerated Pointy-Haired Cat (TM):www.chiark.greenend.org.uk/~davidr/ it's like a cat that's completely
> clueless but it's twice as fast!
|
| | |
Date: 11 Oct 2007 15:21:47
From: David Richerby
Subject: Re: Counting knight moves
|
SBD <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Secondly, the moving the knight close to the right direction and
>> then correcting at the end always works. Trying to move in the
>> right direction in a maze might send you completely the wrong way.
>
> Could you give an example of this, because in many chess problems
> that is precisely the problem: you think you are going the correct
> route with the knight but realize you had to "lose a move" or "move
> back then forward".
Alexander's Technique only tells you the answer to the question `What
is the minimum number of moves required to get a knight from A to B on
a completely empty chess board.' My replacement technique has the
same goals. In real life (or even in a puzzle ;-) ) the opponent's
moves and the placement of the other pieces on the board interfere.
Dave.
--
David Richerby Dangerous Poetic Tool (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a hammer but it's in verse and it
could explode at any minute!
|
| |
Date: 11 Oct 2007 10:11:37
From: SBD
Subject: Re: Counting knight moves
|
On Oct 11, 4:46 am, David Richerby <[email protected] >
wrote:
> Alexander's technique sounds to me like a very hard way to do
> something nearly trivial.
Perhaps, but following the conversation, I began to wonder if it might
have value for things like composing long seriesmovers with one or
more knights. And there is an American author who recommends modified
seriesmovers (Albertston, Chess Mazes) for developing tactical vision.
You are probably correct it that it is a triviality, but it is one
that might have specific uses. Or not. :)
|
| | |
Date: 11 Oct 2007 11:35:50
From: David Richerby
Subject: Re: Counting knight moves
|
SBD <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Alexander's technique sounds to me like a very hard way to do
>> something nearly trivial.
>
> Perhaps, but following the conversation, I began to wonder if it
> might have value for things like composing long seriesmovers with
> one or more knights. And there is an American author who recommends
> modified seriesmovers (Albertston, Chess Mazes) for developing
> tactical vision.
It might be useful for that, yes. The only other suggestion was for
knight endgames but there, the whole point is that the enemy king can
move. If knight endgames were as simple as `If he doesn't move his
king, I can cut off that pawn with my knight', well, they'd be much
simpler than they are.
Dave.
--
David Richerby Expensive Radioactive Umbrella (TM):
www.chiark.greenend.org.uk/~davidr/ it's like an umbrella but it'll
make you glow in the dark and break
the bank!
|
| |
Date: 10 Oct 2007 10:20:14
From: foot
Subject: Re: Counting knight moves
|
On Tue, 09 Oct 2007 12:07:33 -0700
Richard <[email protected] > wrote:
>
> I've got to agree with Mr. Richerby on this one. I've heard of niche
> books on specific skills, but this seems like something that should
> take up 5 pages of a book on many more topics, not something that
> should have its own 80 page book.
As I've said several times now, the part of the book that teaches the
method only takes up 8 pages! About 40 pages of the book explain why
the method works. The rest are examples, exercises, answers,
reference, and index. And I'm happy these are there, because they
make learning the method easier, and learning why it works is
interesting.
> As for how I learned stuff like this, I learned it the hard way. In
> playing, I quickly learned that a knight takes two moves to move to a
> square diagonally next to it. From playing and doing some exercises
> that I saw recommended somewhere to improve "board vision", I figured
> out that it takes 3 moves to move a knight to the square next to it.
> And I think it probably through actual play that I realized that going
> to the opposite corner of a 3x3 square takes an annoyingly long number
> of moves, which ends up being 4, so I try to avoid those situations
> where possible.
Well, it's great that you learned that on your own. But perhaps you'll
forgive others for not wanting to go about this the hard way, and for
wanting to learn even more rules about knight moves besides the ones
described in this thread.
|
| | |
Date: 11 Oct 2007 10:46:55
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> Richard <[email protected]> wrote:
>> I've got to agree with Mr. Richerby on this one. I've heard of niche
>> books on specific skills, but this seems like something that should
>> take up 5 pages of a book on many more topics, not something that
>> should have its own 80 page book.
>
> As I've said several times now, the part of the book that teaches the
> method only takes up 8 pages!
This is obviously some strange new meaning of the word `only' of which
I was previously unaware. Mine took less than half a page.
> Well, it's great that you learned that on your own. But perhaps
> you'll forgive others for not wanting to go about this the hard way,
> and for wanting to learn even more rules about knight moves besides
> the ones described in this thread.
Alexander's technique sounds to me like a very hard way to do
something nearly trivial.
Dave.
--
David Richerby Erotic Sumerian Drink (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a refreshing juice beverage that's
really old but it's genuinely erotic!
|
| |
Date: 09 Oct 2007 15:15:12
From: foot
Subject: Re: Counting knight moves
|
On 09 Oct 2007 18:10:20 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> foot <[email protected]> wrote:
> > David Richerby <[email protected]> wrote:
> >> foot <[email protected]> wrote:
> >>> How do you know there's no two-move route [from g6 to e4]?
> >> Because any knight move from g6 either puts the knight on a square
> >> adjacent to e4 (f4 or e5) or on a square a long way from e4.
> >
> > So, when you say "any knight move", you're pretty much admitting
> > that you checked to see where every knight move landed.
>
> Absolutely not! Two moves are too close; all the others are too far
> away. I don't need to think about which squares a knight can move to
> from g6: it's instantly obvious to me. It's also instantly obvious
> that none of those squares is a knight's move from e4. I don't
> believe I have any extraordinary skill here.
Well, it's certainly not instantly obvious to me. I either have to use
Alexander's Technique, or rely on trial and error. I have no magic
sixth-sense that will tell me that two moves couldn't get me from g6 to
e4. For all I know, perhaps they could. That uncertainty would
ordinarily lead me to try some two-move paths before being convinced
that a two-move path couldn't get me there.
If it's really true that you don't need to do the same, engaging in
trial and error moves, then that's great for you. But I don't think
the average chess player is so gifted.
And the problem becomes much worse with longer move paths.
> > Your method will find that moving to a certain square will take a
> > minimum of 5 moves in a second or two? I don't think so.
>
> I think you need to get a much better feel of how the pieces move.
> How do you get on with solving tactics puzzles without moving the
> pieces on the board?
Sometimes having to move pieces is unavoidable. And sometimes, as in
the case of the method taught in this book, moving the pieces is not
necessary (except for the squares which are one knight move away, for
which there is no shortcut).
> > Try using your method to on a square that's a minimum of 5 moves
> > away, like g1 to a6 (the example I meant to give in my last message,
> > but said "h6" for some inexplicable reason).
>
> Again, I had no problems whatsoever getting a knight from g1 to a6 in
> five moves and convincing myself that three is impossible. Heading
> straight for a6 puts you on c3/d4/e5 after two moves and a4/b5/c6/d7
> after three. All of those squares are two moves from a6; if you can't
> instantly see that they are, you really need to work on your
> visualization.
If you asked me whether a4 was a minimum of three moves away, I couldn't
instantly tell you whether it was or not without using Alexander's
Technique. I'd have to try moving there: the trial and error method.
It certainly wouldn't be "obvious" to me that that square was a minimum
of three moves away the way it's obvious to me that f3 is one move away
from g1. And I suspect the same would hold for most other chess
players.
> (I'm not claiming that I computed all of that in my
> head to work out the move-count. I just mean that the squares I gave
> are the places you could get to from your interpretation of `start at
> g1 and head straight for a6.)
Well, let's say you did head "straight for a6" from g1... and you went
to f3-d4-b5 and now where? Well, it's anyone's guess! Let's try c3,
and then where? Well, maybe a4, and then b6 or c5. Well, you're
already beyond the minimum of 5 moves, and you haven't even reached
your destination square.
So, maybe you backtrack to c3 and then to d5 instead of a4, and then
where? Maybe you could try b4, b6, or c7... none of which get you to
b5 in the minimum of five moves. And then, can you really be sure that
when you backtracked c3 was one of the squares you'd moved your knight
to initially? Maybe it's better to start from the beginning... more
time wasted.
So I don't think it's all as neat and simple as you make it out to be...
at least not for the longer knight paths. That is, unless you happen
to luck on to the shortest path on the first try. And, even then,
you can't be sure the path you lucked on to is indeed the shortest path
without trying to get there in fewer moves... which means more time
wasted and more opportunity for error and confusion.
> > With your method, it sounds like there will be trial and error
> > involved, and you will be left guessing as to whether there is
> > actually a shorter route that you might be missing.
>
> a6 is just too far from g1 to get there in three moves. The closest
> you can get on the a-file in three moves is a4 because you need to
> move two squares left on each move to get to the a-file, so you're
> only moving one square up. Again, this is post-hoc rationalization;
> it's just obviously too far as soon as moving towards the target
> square for three moves leave you short.
Right... so you do need to try moving there to see that it's too far...
another matter of trial and error that the method taught in the book
make unnecessary. It's just a matter of looking at the board, applying
a simple rule, and the result is that you know a6 is 5 moves from g1.
No need to try candidate paths with the knight.
> > With the method taught in the book there is no guessing or trial and
> > error. It's just a matter of applying a rule sort of like your
> > "Moving to the opposite corner of a 3x3 square always takes four
> > moves," only the rule will apply for squares which are a minimum of
> > 5 moves away.
>
> But the technique involves applying eight pages of rules that have
> nothing to do with chess per se.
What does it matter whether the rules "have to do with chess per se" (a
point that could be debated.. but I don't want to go there) ? As long
as it works, works quickly, and eliminates the possibility of error and
confusion?
> My technique just involved playing chess and knowing a couple of
> special cases.
Parts of your technique are actually pretty similar to what's taught in
the book, so if you don't have any problem using your technique then
you shouldn't have a problem with the technique taught in the book,
which is pretty similar. However, the technique in the book eliminates
the need for trial and error moves of the knight (except for the
squares which are only one move away, for which there is no shortcut).
> You're dismissing guessing as leading to inaccurate answers. My point
> is that, having made an educated guess, it's very easy to confirm that
> one's guess is correct.
Well, it might be easy to confirm whether there is a path that's as long
as what you've guessed (assuming you luck on to the correct path on
your first try, and not get confused and led off track, as in the g1 to
a6 path example I gave above)... but verifying that what you've guessed
is indeed the shortest possible path to the destination square might
not be so easy. You might be forced to try a number (perhaps even a
large number) of alternate paths. In any event, there's always the
possibility of error and confusion, and it will take time to verify
your guess.
With the book method there is no guessing.
> Your method tells you that g1 to a6 is five moves, as an abstract,
> uninterpreted fact. You're still going to have to use what you call
> `trial and error' in order to find out if any of the five-move paths
> is available to you on the board.
That assumes that you're interested in that information. Perhaps,
knowing that a certain square is a minimum of 5 moves away is enough.
For example, say you have a pawn on a4 that will queen in 4 moves. You
opponent has a knight on g1. Will he be able to stop your pawn? You
apply the method and virtually immediately know that it will take that
knight at least 5 moves to get to a8. So you don't even care what path
he's going to try to get there. You can confidently ch your pawn
forward.
> I'm glad it worked for you. I think the time would have been better
> spend improving your visualization skills so you could see these
> things without needing fancy techniques.
It's not a "fancy" technique. At least, no more "fancy" than your own
method, which is quite similar (though lacking in that parts of it
still require you to try moving your knight to various squares).
I really don't see the need to use pejorative terms like "fancy" in
regards to something you have no knowledge of. It's really quite
amazing how some people will put up a tremendous amount of resistance
and hostility to learning anything new.
You know, I actually like learning new things. When there's something
new to learn that gets me interested and excited. I thought by
mentioning that there was something new, interesting and useful to learn
I'd get positive reactions from this group. Instead all I got was
invective from people who apparently can't be bothered to learn
anything new. I think that's pretty sad.
|
| | |
Date: 11 Oct 2007 13:45:46
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> Again, I had no problems whatsoever getting a knight from g1 to a6 in
>> five moves and convincing myself that three is impossible. Heading
>> straight for a6 puts you on c3/d4/e5 after two moves and a4/b5/c6/d7
>> after three. All of those squares are two moves from a6; if you can't
>> instantly see that they are, you really need to work on your
>> visualization.
>
> If you asked me whether a4 was a minimum of three moves away, I
> couldn't instantly tell you whether it was or not without using
> Alexander's Technique.
I'm pretty sure you said that Alexander's Technique was taking you ten
to fifteen seconds. That's not instant. Now, I couldn't tell you
*instantly* but after making the attempt g1-e2-b3-a4, it should be
obvious that you can't get any closer than that in three moves. That
wouldn't have taken me more than a couple of seconds.
>> (I'm not claiming that I computed all of that in my head to work
>> out the move-count. I just mean that the squares I gave are the
>> places you could get to from your interpretation of `start at g1
>> and head straight for a6.)
>
> Well, let's say you did head "straight for a6" from g1... and you
> went to f3-d4-b5 and now where?
b5 and a6 are diagonally adjacent! b5-c7-a6. If you can't see the
two-move path between diagonally adjacent squares, I can understand
why you're reluctant to use my trial-and-error method. I assure you
that I'm not a gifted chess player -- I'm doing absolutely nothing
special.
It seems to me that you have very poor board vision. Are you a new
player? You also mentioned that you sometimes find it essential to
move the pieces to solve tactical problems. Perhaps you're trying
problems beyond your current ability but how are you going to choose
good moves during games, where you're not allowed to move the pieces
around while you think? I'd recommend that, rather than learning
specialist techniques for counting knight moves, you concentrate on
improving your board vision by doing lots of tactics puzzles, all in
your head. It will be slow going at first but you'll find you get
better at it and that this will dramatically increase your strength.
>> But the technique involves applying eight pages of rules that have
>> nothing to do with chess per se.
>
> What does it matter whether the rules "have to do with chess per se"
> (a point that could be debated.. but I don't want to go there) ? As
> long as it works, works quickly, and eliminates the possibility of
> error and confusion?
The advantage of chess-based reasoning is that it help your
understanding of other parts of the game and reinforces your ability
to calculate in your head. Other rules can't be applied to anything
else.
> For example, say you have a pawn on a4 that will queen in 4 moves.
> You opponent has a knight on g1. Will he be able to stop your pawn?
> You apply the method and virtually immediately know that it will
> take that knight at least 5 moves to get to a8. So you don't even
> care what path he's going to try to get there. You can confidently
> ch your pawn forward.
But knight endgames aren't that simple! Where's his king? Can it
stop the pawn? Can he gain a tempo by checking you with his knight on
the way to a8? (An extremely important resource in knight endgames.)
If your king's on b5/c4/d5/d7/e6/e8, it's enough for him to get his
knight to b6/c7 immediately after you promote, forking your king and
new queen. (Another important resource) Or will you be promoting with
check so he doesn't have time to do that?
> I really don't see the need to use pejorative terms like "fancy" in
> regards to something you have no knowledge of. It's really quite
> amazing how some people will put up a tremendous amount of
> resistance and hostility to learning anything new.
I'm resistant to learning a slower, more cumbersome way to do
something which I can already do and feel that any chess player beyond
a beginner should be able to do.
> You know, I actually like learning new things.
So do I. I'm an academic -- it's even my job to learn new things!
> When there's something new to learn that gets me interested and
> excited. I thought by mentioning that there was something new,
> interesting and useful to learn I'd get positive reactions from this
> group. Instead all I got was invective from people who apparently
> can't be bothered to learn anything new. I think that's pretty sad.
I don't think this technique is either interesting or useful: that's
the point I've been making. It's not that I can't be bothered to
learn it; I've looked at it (through your descriptions) and found it
to be not worth the time or effort. I don't even think the technique
is helping you very much, either, since it seems that you have great
difficulty using your knowledge that there's a five-move path between
two squares to actually find such a path -- that's what I think you
should be spending your time working on.
I'm sorry if my criticism of the technique you've been advancing came
across as criticism of you. It probably sounded like it was but it
wasn't intended as such.
Dave.
--
David Richerby Radioactive Postman (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a man who delivers the mail but it'll
make you glow in the dark!
|
| |
Date: 09 Oct 2007 12:07:33
From: Richard
Subject: Re: Counting knight moves
|
On Oct 9, 11:33 am, foot <[email protected] > wrote:
> And, by the way, how did you know that "Moving to the opposite corner
> of a 3x3 square always takes four moves." Did you, perhaps, read this
> in a book? Did you figure it out yourself? Or did someone teach you?
> (someone who themselves probably read it in a book) If it was,
> directly, or indirectly, received from a book, how can you maintain
> that such a book is useless?
>
I've got to agree with Mr. Richerby on this one. I've heard of niche
books on specific skills, but this seems like something that should
take up 5 pages of a book on many more topics, not something that
should have its own 80 page book.
As for how I learned stuff like this, I learned it the hard way. In
playing, I quickly learned that a knight takes two moves to move to a
square diagonally next to it. From playing and doing some exercises
that I saw recommended somewhere to improve "board vision", I figured
out that it takes 3 moves to move a knight to the square next to it.
And I think it probably through actual play that I realized that going
to the opposite corner of a 3x3 square takes an annoyingly long number
of moves, which ends up being 4, so I try to avoid those situations
where possible.
--Richard
|
| |
Date: 09 Oct 2007 12:57:18
From: foot
Subject: Re: Counting knight moves
|
On Tue, 09 Oct 2007 09:42:58 -0700
Taylor Kingston <[email protected] > wrote:
>
> This may be of interest as an intellectual exercise or parlor trick,
> but its utility in practical play seems rather limited. I suppose it
> might save some calculating time in an unusual endgame where it was
> critical to get a knight to a distant square in the fewest moves,
I don't think this is unusual at all. I've played many endgames myself
where doing just this was important. Using a knight to try to stop a
pawn from queening is relatively common. Sure, it doesn't happen in
every endgame, but I think it happens often enough that improving one's
technique would be useful, and certainly more than a "parlour trick".
> but in most real-game positions, especially in the middle game, any
> moderately experienced player can plot a knight's optimal path with
> ease.
Most middlegame knight moves aren't very lengthy, so in general I
agree. But sometimes you do want to get a knight from the queenside
to the kingside (or perhaps to an adjacent square, which can sometimes
take up to four moves), and this method will quickly and reliably tell
you what the minimum number of moves such a path must take. I think
this is also useful... though I suppose some people might be satisfied
with just using a trial and error method.
> Does Alexander claim his technique is of much practical use?
Well, here's the blurb from the back of the book. (I don't know if
this was written by Alexander or his publisher)
"Knight moves are the most difficult to visualize on the chess board.
In the endgame it is frequently necessary to determine whether a knight
can reach a certain square to intercept a passed pawn or protect one of
your own pieces or pawns. In the time pressure of many tournament
endgames, it is even more difficult to concentrate and feel confident
that you have correctly calculated the possible path of the knight and
the number of moves necessary in the variation. This often leads a
player to repeat the sequence in the mind a number of times to feel
certain that his projected moves will indeed accomplish the objective.
Mr. Alexander has developed a set of tools which make it very precise
and quick to determine the required number of moves, and whether or not
a sequence of knight moves will achieve a goal. The author has
developed a wonderful set of graphs which visualize the possibilities
of moving a knight to a desired goal. Many players will find this
technique to be invaluable in winning endgames involving the knight, or
even combinations in the course of the middlegame."
|
| | |
Date: 11 Oct 2007 14:01:11
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> Well, here's the blurb from the back of the book. (I don't know if
> this was written by Alexander or his publisher)
Blurb is almost always written by the publisher, to maximize sales by
making the book sound as exciting and useful as possible.
Dave.
--
David Richerby Permanent Bulb (TM): it's like a light
www.chiark.greenend.org.uk/~davidr/ bulb but it'll be there for ever!
|
| |
Date: 09 Oct 2007 12:45:49
From: foot
Subject: Re: Counting knight moves
|
On 09 Oct 2007 17:33:33 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> > If it was, directly, or indirectly, received from a book, how can
> > you maintain that such a book is useless?
>
> Perhaps it was from a book. But if it was, it was a book that
> happened to contain this information and much more besides, not a book
> specifically about how to get a knight from A to B.
Why do you object to niche chess books? If they achieve what they set
out to do, what's the problem?
> > I never claimed you had to read the entire eighty-page book to learn
> > the methods within. In fact, in my review I explicitly said that
> > you'd only need to read about 8 pages of it to learn the method.
>
> Well, yes. But it's still an eighty page book and it's still eight
> pages to describe how to do something trivial.
I don't think it's trivial. Nor do I think most chess players would
find it trivial. I think the book could have been shorter (by
omitting the first half that describes why the method works), but then
it would have been less interesting. It could have also been shortened
by taking out the examples, exercises, and diagrams, but then it would
have made learning the method harder. So, I think it's really the
perfect length.
> > I, for one, am glad the author didn't try to cram the whole method
> > in to a single page, without any examples, explanations, exercises,
> > diagrams, or answers... as I would have probably had a harder time
> > learning it.
>
> Of course. And it may well be an especially well-written book that
> explains the method extremely well. But it still strikes me as being
> like a book that teaches you enough rock-climbing skills to let you
> get to the second floor of your house by scaling the outside wall and
> coming in through the window, rather than just telling you to walk up
> the stairs.
Well, the trial and error parts of the method you describe is not like
"walking up the stairs", but more like trying to solve a maze by
randomly picking directions, instead of always making right hand turns.
But, hey, it works for you... and you seem to be in no hurry to improve
on it. Fine. But I do think that many other chess players will be
interested in learning a better way.
|
| | |
Date: 11 Oct 2007 13:58:49
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>>> If it was, directly, or indirectly, received from a book, how can
>>> you maintain that such a book is useless?
>>
>> Perhaps it was from a book. But if it was, it was a book that
>> happened to contain this information and much more besides, not a
>> book specifically about how to get a knight from A to B.
>
> Why do you object to niche chess books? If they achieve what they set
> out to do, what's the problem?
I object to this book because any reasonable player can already
calculate quickly and accurately the number of moves it would take a
knight to get between two squares. Any weaker player would be better
served by improving their board vision until they can calculate this
using their chess skill, rather than learning the technique.
>> But it's still an eighty page book and it's still eight pages to
>> describe how to do something trivial.
>
> I don't think it's trivial. Nor do I think most chess players would
> find it trivial.
I assure you that I'm just an ordinary player. I have no especial
skill at the game.
> Well, the trial and error parts of the method you describe is not
> like "walking up the stairs", but more like trying to solve a maze
> by randomly picking directions, instead of always making right hand
> turns.
No, for two reasons. Firstly, I'm not advocating moving randomly.
Secondly, the moving the knight close to the right direction and then
correcting at the end always works. Trying to move in the right
direction in a maze might send you completely the wrong way.
The walking up the stairs analogy wasn't intended as a direct analogy
but just an indication that advanced techniques really aren't needed.
> But, hey, it works for you... and you seem to be in no hurry to
> improve on it.
I'm in no hurry to improve because I can already get the correct
answer faster than I could using the technique and at least as
accurately. The technique just isn't an improvement.
Dave.
--
David Richerby Accelerated Pointy-Haired Cat (TM):
www.chiark.greenend.org.uk/~davidr/ it's like a cat that's completely
clueless but it's twice as fast!
|
| |
Date: 09 Oct 2007 09:42:58
From: Taylor Kingston
Subject: Re: Counting knight moves
|
On Oct 9, 11:33 am, foot <[email protected] > wrote:
> And, by the way, how did you know that "Moving to the opposite corner
> of a 3x3 square always takes four moves." Did you, perhaps, read this
> in a book? Did you figure it out yourself? Or did someone teach you?
> (someone who themselves probably read it in a book) If it was,
> directly, or indirectly, received from a book, how can you maintain
> that such a book is useless?
>
> On 09 Oct 2007 11:21:14 +0100 (BST) David Richerby
>
> <[email protected]> wrote:
>
> > I'll admit to being utterly flabbergasted as to why somebody would
> > write an eighty-page book explaining how to do something this simple.
>
> I never claimed you had to read the entire eighty-page book to learn
> the methods within. In fact, in my review I explicitly said that you'd
> only need to read about 8 pages of it to learn the method. The rest of
> the book explains why the method works, provides examples, exercises,
> answers, reference, and index... with lots of diagrams to boot. All
> this makes the method easier to learn.
>
> I, for one, am glad the author didn't try to cram the whole method in
> to a single page, without any examples, explanations, exercises,
> diagrams, or answers... as I would have probably had a harder time
> learning it.
>
> Anyway, no one will force you to read the entire book. You can read as
> much or as little of it as you find useful.
This may be of interest as an intellectual exercise or parlor trick,
but its utility in practical play seems rather limited. I suppose it
might save some calculating time in an unusual endgame where it was
critical to get a knight to a distant square in the fewest moves, but
in most real-game positions, especially in the middle game, any
moderately experienced player can plot a knight's optimal path with
ease. Does Alexander claim his technique is of much practical use?
|
| |
Date: 09 Oct 2007 11:33:33
From: foot
Subject: Re: Counting knight moves
|
And, by the way, how did you know that "Moving to the opposite corner
of a 3x3 square always takes four moves." Did you, perhaps, read this
in a book? Did you figure it out yourself? Or did someone teach you?
(someone who themselves probably read it in a book) If it was,
directly, or indirectly, received from a book, how can you maintain
that such a book is useless?
On 09 Oct 2007 11:21:14 +0100 (BST) David Richerby
<[email protected] > wrote:
>
> I'll admit to being utterly flabbergasted as to why somebody would
> write an eighty-page book explaining how to do something this simple.
I never claimed you had to read the entire eighty-page book to learn
the methods within. In fact, in my review I explicitly said that you'd
only need to read about 8 pages of it to learn the method. The rest of
the book explains why the method works, provides examples, exercises,
answers, reference, and index... with lots of diagrams to boot. All
this makes the method easier to learn.
I, for one, am glad the author didn't try to cram the whole method in
to a single page, without any examples, explanations, exercises,
diagrams, or answers... as I would have probably had a harder time
learning it.
Anyway, no one will force you to read the entire book. You can read as
much or as little of it as you find useful.
|
| | |
Date: 09 Oct 2007 17:33:33
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> And, by the way, how did you know that "Moving to the opposite
> corner of a 3x3 square always takes four moves."
I honestly can't remember. It's something I've known `forever', so to
speak.
> If it was, directly, or indirectly, received from a book, how can
> you maintain that such a book is useless?
Perhaps it was from a book. But if it was, it was a book that
happened to contain this information and much more besides, not a book
specifically about how to get a knight from A to B.
> David Richerby <[email protected]> wrote:
>> I'll admit to being utterly flabbergasted as to why somebody would
>> write an eighty-page book explaining how to do something this
>> simple.
>
> I never claimed you had to read the entire eighty-page book to learn
> the methods within. In fact, in my review I explicitly said that
> you'd only need to read about 8 pages of it to learn the method.
Well, yes. But it's still an eighty page book and it's still eight
pages to describe how to do something trivial.
> I, for one, am glad the author didn't try to cram the whole method
> in to a single page, without any examples, explanations, exercises,
> diagrams, or answers... as I would have probably had a harder time
> learning it.
Of course. And it may well be an especially well-written book that
explains the method extremely well. But it still strikes me as being
like a book that teaches you enough rock-climbing skills to let you
get to the second floor of your house by scaling the outside wall and
coming in through the window, rather than just telling you to walk up
the stairs.
Dave.
--
David Richerby Broken Ghost (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ haunting spirit but it doesn't work!
|
| |
Date: 09 Oct 2007 11:20:44
From: foot
Subject: Re: Counting knight moves
|
On 09 Oct 2007 11:21:14 +0100 (BST)
David Richerby <[email protected] > wrote:
>
> >> foot <[email protected]> wrote:
> >>> f8-e6-g5-e4. But is there a shorter route?
> >>=20
> >> Obviously not. e4 and g6 are both white squares so it must take an
> >> even number of moves to get between them. There's clearly no
> >> two-move route so four must be the shortest.
> >
> > How do you know there's no two-move route?
>=20
> Because any knight move from g6 either puts the knight on a square
> adjacent to e4 (f4 or e5) or on a square a long way from e4.
So, when you say "any knight move", you're pretty much admitting that
you checked to see where every knight move landed. You're essentially
mentally checking to see if there's a two-move route.
=46rom what you describe, it sounds like you thought something like:
"g6t o e7, and it's too far from e7 to make it to e4 in one move.
then, g6 to h4, and it's too far from h4 to make it to e4 in one move.
then, g6 to f8, and it's too far from f8 to make it to e4 in one move.
then, g6 to e5, and it's adjacent to e4, so the knight can't make it
from e5 to e4 in one move. then, g6 to f4, which is adjacent to e4, so
the knight can't make it from f4 to e4 in one move."
Once again, this is exactly the kind of trial and error approach the
book's method is supposed to improve upon.
> This really isn't any harder than `How do you know there isn't a
> one-move route for a bishop from g2 to d3?'
I think it is harder. Bishops move in straight lines. Seeing that a
given square is on or off the straight line path leading from a bishop
is a lot easier than the process you seem to have used.
By the way, I'm not claiming that the book's method makes recognizing
the minimum number of moves to every single possible destination square
the knight can get to as easily recognizable as a bishop move, but
there are some squares which studying the book will let you recognize
just as easily, and the others you can figure out without the trial and
error of the sort you seem to be using.
> > You probably tried a number of routes to move your knight from g6 to
> > e4 and found it couldn't get there in two moves.
>=20
> No. It's instantly obvious to me that there's no two-move route. And
> I'm not a strong player; I'm just familiar with how the pieces move.
Well, "obvious" doesn't mean you didn't try every possible single
move route, and then see if a second move can get you to your
destination square.... which is what you apparently did. It may be
"obvious", but it's not very efficient, and it's easy to make a mistake
when you're trying all these possible moves, or at least wind up
wondering if you really tried them all or might need to go back and
re-try them, just to be sure you got it right... which means more time,
and more opportunity for error.
> > But I'd bet most people would take some time to figure these out
> > with any amount of certainty.
>=20
> Maybe so. But here's how to do it and get it right in seconds almost
> every time.
>=20
> Important knowledge
> -------------------
> 1) Moving between two squares of the same colour must take an even
> number of moves.
> 2) Moving between differently coloured squares must take an odd number
> of moves.
>=20
> Special cases
> -------------
> 3) Moving to a diagonally adjacent square takes two moves, unless the
> source or destination is a corner, in which case it takes four.
> 4) Moving to a horizontally or vertically adjacent square always takes
> three moves.
> 5) Moving to the opposite corner of a 3x3 square always takes four
> moves.
Very good. Up to this point, the technique you describe is similar to
what's in the book. However, you still haven't given any rules for
determining if a given square is 3 or 5 moves away (except when the
destination square is a horizontally or vertically adjacent square.
> Technique
> ---------
> 6) To find the fastest route, move towards the destination in as
> straight a line as possible and then use the special cases 3-5 to
> determine the answer once you get close enough.
Ok. Well, now you're back to the trial and error method. There is a
better way than this, and the book teaches it.
> > And if you're comparing how long it would take to get to more than
> > one or two squares then the time spent on these types of
> > calculations can really add up...
>=20
> They really don't. They're so fast that the difference between a
> second or two (getting to one square) and two or three seconds
> (getting to two squares) is negligible. Why would I ever want to know
> how long it takes a knight to get to more than two squares?
Your method will find that moving to a certain square will take a
minimum of 5 moves in a second or two? I don't think so.
> >> And the technique doesn't work when there are other pieces on the
> >> board. Which is to say, all the time.
> >
> > Actually, it does work even when there are other pieces on the
> > board, as what the technique tells you is the **minimum** number of
> > moves that a knight will take to get to any given square.
>=20
> And so does my technique. Much faster. And actually looking for the
> routes will automatically show you which ones are or are not possible.
Try using your method to on a square that's a minimum of 5 moves away,
like g1 to a6 (the example I meant to give in my last message, but said
"h6" for some inexplicable reason). With your method, it sounds like
there will be trial and error involved, and you will be left guessing
as to whether there is actually a shorter route that you might be
missing.
With the method taught in the book there is no guessing or trial and
error. It's just a matter of applying a rule sort of like your
"Moving to the opposite corner of a 3x3 square always takes four
moves," only the rule will apply for squares which are a minimum of 5
moves away.
> > 2, 3, 4, and 5 move paths are much more common, and happen to be the
> > ones where this method becomes most useful.
>=20
> If you have difficulty working out that it takes two moves to get a
> knight between two squares, I really recommend you spend more time
> playing chess and familiarizing yourself with the pieces.
Well, it's not a matter of difficulty. It's a matter of whether you're
figuring out the minimum number of moves it will take a knight to get
to a given square through trial and error and guessing, or whether
you're doing it by applying rules and getting answers you can feel
confident in, and doing it faster than the parts of your method that
involve trial and error.
> I'll admit to being utterly flabbergasted as to why somebody would
> write an eighty-page book explaining how to do something this simple.
Well, I found the book to be extremely useful, and I bet most other
chess players will too. You seem to already know quite a bit more
about moving knights than the average chess player (certainly much more
than I did before I bought the book), so it sounds like the book may
not be the best investment for you (though even for you, I think
the book could teach you some better methods than the ones you're using,
for certain squares on the board, such as the squares 3 and 5 moves
away).
|
| | |
Date: 09 Oct 2007 18:10:20
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> foot <[email protected]> wrote:
>>> How do you know there's no two-move route [from g6 to e4]?
>> Because any knight move from g6 either puts the knight on a square
>> adjacent to e4 (f4 or e5) or on a square a long way from e4.
>
> So, when you say "any knight move", you're pretty much admitting
> that you checked to see where every knight move landed.
Absolutely not! Two moves are too close; all the others are too far
away. I don't need to think about which squares a knight can move to
from g6: it's instantly obvious to me. It's also instantly obvious
that none of those squares is a knight's move from e4. I don't
believe I have any extraordinary skill here.
(To clarify, I'd have to think to name the squares but, looking at a
board, it's completely obvious.)
> Once again, this is exactly the kind of trial and error approach the
> book's method is supposed to improve upon.
I assure you that there is no `trial and error' in determining whether
a knight can get between two squares in two moves. I really can't
conceive of getting it wrong.
>> It's instantly obvious to me that there's no two-move route. And
>> I'm not a strong player; I'm just familiar with how the pieces
>> move.
>
> Well, "obvious" doesn't mean you didn't try every possible single
> move route, and then see if a second move can get you to your
> destination square.... which is what you apparently did.
No! It's just completely obvious. Perhaps my post-hoc rationaliz-
ation of why it's obvious misled you into thinking that I'd tried all
the possible first moves and discarded them one by one.
> Your method will find that moving to a certain square will take a
> minimum of 5 moves in a second or two? I don't think so.
I think you need to get a much better feel of how the pieces move.
How do you get on with solving tactics puzzles without moving the
pieces on the board?
> Try using your method to on a square that's a minimum of 5 moves
> away, like g1 to a6 (the example I meant to give in my last message,
> but said "h6" for some inexplicable reason).
Again, I had no problems whatsoever getting a knight from g1 to a6 in
five moves and convincing myself that three is impossible. Heading
straight for a6 puts you on c3/d4/e5 after two moves and a4/b5/c6/d7
after three. All of those squares are two moves from a6; if you can't
instantly see that they are, you really need to work on your
visualization. (I'm not claiming that I computed all of that in my
head to work out the move-count. I just mean that the squares I gave
are the places you could get to from your interpretation of `start at
g1 and head straight for a6.)
> With your method, it sounds like there will be trial and error
> involved, and you will be left guessing as to whether there is
> actually a shorter route that you might be missing.
a6 is just too far from g1 to get there in three moves. The closest
you can get on the a-file in three moves is a4 because you need to
move two squares left on each move to get to the a-file, so you're
only moving one square up. Again, this is post-hoc rationalization;
it's just obviously too far as soon as moving towards the target
square for three moves leave you short.
> With the method taught in the book there is no guessing or trial and
> error. It's just a matter of applying a rule sort of like your
> "Moving to the opposite corner of a 3x3 square always takes four
> moves," only the rule will apply for squares which are a minimum of
> 5 moves away.
But the technique involves applying eight pages of rules that have
nothing to do with chess per se. My technique just involved playing
chess and knowing a couple of special cases.
You're dismissing guessing as leading to inaccurate answers. My point
is that, having made an educated guess, it's very easy to confirm that
one's guess is correct.
Your method tells you that g1 to a6 is five moves, as an abstract,
uninterpreted fact. You're still going to have to use what you call
`trial and error' in order to find out if any of the five-move paths
is available to you on the board.
>> I'll admit to being utterly flabbergasted as to why somebody would
>> write an eighty-page book explaining how to do something this
>> simple.
>
> Well, I found the book to be extremely useful, and I bet most other
> chess players will too.
I'm glad it worked for you. I think the time would have been better
spend improving your visualization skills so you could see these
things without needing fancy techniques.
Dave.
--
David Richerby Flammable Edible Drink (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a refreshing juice beverage but you
can eat it and it burns really easily!
|
| |
Date: 08 Oct 2007 15:41:05
From: foot
Subject: Re: Counting knight moves
|
On 08 Oct 2007 14:13:25 +0100 (BST)
David Richerby <[email protected] > wrote:
> foot <[email protected]> wrote:
> > Quick! What's the minimum number of moves a knight on g6 needs to
> > get to e4 ?
>
> Four. (Bad example -- doesn't everybody know that it takes three
> moves to get a knight to a horizontally/vertically adjacent square
> and four moves to get to the opposite corner of a 3x3 square,
> anywhere on the board?)
No. I don't think everyone knows that. In fact, I'd bet that most
chess players don't know that. And they probably don't know any other
techniques for determining the minimum number of moves required for
a knight to get from one given square to another.
> > To answer this question, most chess players will simply start to
> > mentally move their knight around, counting the moves, until it
> > lands on the desired square. Let's say you counted 4 moves:
> > e5-g4-f6-e4 That's one way to get there, and so is: f8-e6-g5-e4.
> > But is there a shorter route?
>
> Obviously not. e4 and g6 are both white squares so it must take an
> even number of moves to get between them. There's clearly no two-move
> route so four must be the shortest.
How do you know there's no two-move route? You probably tried a
number of routes to move your knight from g6 to e4 and found it
couldn't get there in two moves. That's exactly the kind of trial and
error approach that the technique taught in this book is designed to
improve on.
> I realise this is a specific case but the same kind of reasoning
> will almost always tell you that there's no shorter route.
It's good that you are able to reason about the moves a knight makes,
at least to a certain extent. You might want to try doing the same
with 5 and 3 move squares before you write this method off, though.
> Nonetheless, Alexander's technique sounds like a total waste of time,
> to me. The fact that a shorter path must be at least two moves
> shorter makes it very easy to count the number of moves on an empty
> board: your first guess is almost certainly right.
Whether you're able to guess right without using the techniques in this
book really depends on where the knight is and where your desired
square is. Try guessing the number of knight moves required to go from
h1 to g2, or g1 to h6. You might be surprised. Or not. In which case,
this book is not for you. But I'd bet most people would take some time
to figure these out with any amount of certainty. And if you're
comparing how long it would take to get to more than one or two squares
then the time spent on these types of calculations can really add up...
especially if you want to do more than just guess.
> And the technique doesn't work when there are other pieces on the board.
> Which is to say, all the time.
Actually, it does work even when there are other pieces on the board,
as what the technique tells you is the **minimum** number of moves that
a knight will take to get to any given square. In other words, using
this technique you'll know that it will never take less than this
number of moves for a knight to get to its destination square. Of
course, it could always take more, depending on the situation on the
board, but even if there are other pieces on the board, that doesn't
mean they're going to necessarily affect the knight's path to where
it's going. It really depends on the position.
> It only takes a moment to see that corner-to-corner can be done in
> six moves. Can it be done in fewer? No, because a knight moves a
> distance sqrt(5) (about 2.24 squares) on each turn, so can move at
> most 8.94 squares in four turns. By Pythagoras, the distance
> corner-to-corner is sqrt(49+49), about 9.90 squares. Obviously,
> you're not going to work that out over the board but, even heading as
> directly as possible for the opposite corner (e.g., a1-c2-d4-f5-g7)
> leaves you a square short. And how likely are you to find an
> eight-move corner-to-corner path? a1-c2-b4-d3-c5-e4-d6-f7-h8 is
> hardly the first thing you'd try.
Well, the path from one corner to the diagonally opposite corner is
really a "corner case" (pardon the pun), in that this kind of route
doesn't happen very often at all. 2, 3, 4, and 5 move paths are much
more common, and happen to be the ones where this method becomes most
useful.
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Date: 09 Oct 2007 11:21:14
From: David Richerby
Subject: Re: Counting knight moves
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foot <[email protected] > wrote:
> David Richerby <[email protected]> wrote:
>> (Bad example -- doesn't everybody know that it takes three moves to
>> get a knight to a horizontally/vertically adjacent square and four
>> moves to get to the opposite corner of a 3x3 square, anywhere on
>> the board?)
>
> No. I don't think everyone knows that. In fact, I'd bet that most
> chess players don't know that.
Really? I'll admit that I had to check that the statement is true
around the edges of the board.
>> foot <[email protected]> wrote:
>>> f8-e6-g5-e4. But is there a shorter route?
>>
>> Obviously not. e4 and g6 are both white squares so it must take an
>> even number of moves to get between them. There's clearly no two-move
>> route so four must be the shortest.
>
> How do you know there's no two-move route?
Because any knight move from g6 either puts the knight on a square
adjacent to e4 (f4 or e5) or on a square a long way from e4.
This really isn't any harder than `How do you know there isn't a
one-move route for a bishop from g2 to d3?'
> You probably tried a number of routes to move your knight from g6 to
> e4 and found it couldn't get there in two moves.
No. It's instantly obvious to me that there's no two-move route. And
I'm not a strong player; I'm just familiar with how the pieces move.
>> Nonetheless, Alexander's technique sounds like a total waste of
>> time, to me. The fact that a shorter path must be at least two
>> moves shorter makes it very easy to count the number of moves on an
>> empty board: your first guess is almost certainly right.
>
> Whether you're able to guess right without using the techniques in
> this book really depends on where the knight is and where your
> desired square is.
Disagree. It really isn't at all difficult.
> Try guessing the number of knight moves required to go from h1 to g2
Four: that's not a guess but an instant calculation. My reasoning is
that any move from h1 puts the knight on a square horizontally or
vertically adjacent to g2 and it takes three moves to get a knight
between horizontally or vertically adjacent squares.
> or g1 to h6.
Four again; calculated in at most two seconds. Reasoning: h6 is too
far away to be able to get there in two moves (it's not possible to
get beyond the fifth rank) and g1-h3-g5-f7-h6 gets there in four.
> But I'd bet most people would take some time to figure these out
> with any amount of certainty.
Maybe so. But here's how to do it and get it right in seconds almost
every time.
Important knowledge
-------------------
1) Moving between two squares of the same colour must take an even
number of moves.
2) Moving between differently coloured squares must take an odd number
of moves.
Special cases
-------------
3) Moving to a diagonally adjacent square takes two moves, unless the
source or destination is a corner, in which case it takes four.
4) Moving to a horizontally or vertically adjacent square always takes
three moves.
5) Moving to the opposite corner of a 3x3 square always takes four
moves.
Technique
---------
6) To find the fastest route, move towards the destination in as
straight a line as possible and then use the special cases 3-5 to
determine the answer once you get close enough.
7) Avoid putting yourself on the opposite corner of a 3x3 square from
your destination if at all possible.
(For example, if you want to go from a1 to d5, don't move to b3
because it will take four more moves to get to d5. Instead, move to
c2, then b4 and d5 -- three moves.)
If you're wrong, you have to be wrong by at least two moves (points 1
and 2) and that's pretty hard to do.
> And if you're comparing how long it would take to get to more than
> one or two squares then the time spent on these types of
> calculations can really add up...
They really don't. They're so fast that the difference between a
second or two (getting to one square) and two or three seconds
(getting to two squares) is negligible. Why would I ever want to know
how long it takes a knight to get to more than two squares?
>> And the technique doesn't work when there are other pieces on the
>> board. Which is to say, all the time.
>
> Actually, it does work even when there are other pieces on the
> board, as what the technique tells you is the **minimum** number of
> moves that a knight will take to get to any given square.
And so does my technique. Much faster. And actually looking for the
routes will automatically show you which ones are or are not possible.
>> It only takes a moment to see that corner-to-corner can be done in
>> six moves. Can it be done in fewer? No, because [argument using
>> Euclidean distance].
>
> Well, the path from one corner to the diagonally opposite corner is
> really a "corner case" (pardon the pun), in that this kind of route
> doesn't happen very often at all.
Of course. I wouldn't have dared to use such a crazy method as
calculating Euclidean distances if I thought people might need to do
this often. :-)
> 2, 3, 4, and 5 move paths are much more common, and happen to be the
> ones where this method becomes most useful.
If you have difficulty working out that it takes two moves to get a
knight between two squares, I really recommend you spend more time
playing chess and familiarizing yourself with the pieces. I hope that
doesn't sound patronizing; it isn't meant to.
I'll admit to being utterly flabbergasted as to why somebody would
write an eighty-page book explaining how to do something this simple.
Dave.
--
David Richerby Simple Painting (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ Renaissance masterpiece but it has no
moving parts!
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Date: 08 Oct 2007 14:13:25
From: David Richerby
Subject: Re: Counting knight moves
|
foot <[email protected] > wrote:
> Quick! What's the minimum number of moves a knight on g6 needs to get
> to e4 ?
Four. (Bad example -- doesn't everybody know that it takes three
moves to get a knight to a horizontally/vertically adjacent square and
four moves to get to the opposite corner of a 3x3 square, anywhere on
the board?)
> To answer this question, most chess players will simply start to
> mentally move their knight around, counting the moves, until it lands
> on the desired square. Let's say you counted 4 moves: e5-g4-f6-e4
> That's one way to get there, and so is: f8-e6-g5-e4. But is there a
> shorter route?
Obviously not. e4 and g6 are both white squares so it must take an
even number of moves to get between them. There's clearly no two-move
route so four must be the shortest. I realise this is a specific case
but the same kind of reasoning will almost always tell you that
there's no shorter route.
Nonetheless, Alexander's technique sounds like a total waste of time,
to me. The fact that a shorter path must be at least two moves
shorter makes it very easy to count the number of moves on an empty
board: your first guess is almost certainly right. And the technique
doesn't work when there are other pieces on the board. Which is to
say, all the time.
It only takes a moment to see that corner-to-corner can be done in
six moves. Can it be done in fewer? No, because a knight moves a
distance sqrt(5) (about 2.24 squares) on each turn, so can move at
most 8.94 squares in four turns. By Pythagoras, the distance
corner-to-corner is sqrt(49+49), about 9.90 squares. Obviously,
you're not going to work that out over the board but, even heading as
directly as possible for the opposite corner (e.g., a1-c2-d4-f5-g7)
leaves you a square short. And how likely are you to find an
eight-move corner-to-corner path? a1-c2-b4-d3-c5-e4-d6-f7-h8 is
hardly the first thing you'd try.
Dave.
--
David Richerby Mouldy Zen Widget (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ thingy that puts you in touch with
the universe but it's starting to
grow mushrooms!
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