Positions with the most legal moves

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Date:
From: Martin Brown
Subject: Positions with the most legal moves

Date: 16 Nov 2006 10:18:56
From: pianowow
Subject: Re: Positions with the most legal moves

[email protected] wrote:
> The composition of Nenad Petrovic in 1964 holds the record of the most
> possible legal moves with its 218 moves!
>
> R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1
>
Am I missing something here? I set up this position and counted only
217... twice.

Knights can move 8 squares
Bishops 10
Rooks 19
King 4
Queens 21, 19, 21, 15, 18, 21, 25, 19, and 17.
(in order d7, b6, c4, a3, d2, f3, e5, g6, h4)
Total is 217.

Date: 20 Nov 2006 09:17:35
From: David Richerby
Subject: Re: Positions with the most legal moves

pianowow <[email protected] > wrote:
>[email protected] wrote:
>> The composition of Nenad Petrovic in 1964 holds the record of the most
>> possible legal moves with its 218 moves!
>>
>> R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1
>>
> Am I missing something here? I set up this position and counted only
> 217... twice.
>
> Knights can move 8 squares
> Bishops 10
> Rooks 19
> King 4
> Queens 21, 19, 21, 15, 18, 21, 25, 19, and 17.
> (in order d7, b6, c4, a3, d2, f3, e5, g6, h4)

The queen on c4 can move to 22 squares, not 21 (perhaps you forgot
Qc4xa2# ?).

Dave.

--
David Richerby Radioactive Zen Vomit (TM): it's like
www.chiark.greenend.org.uk/~davidr/ a pile of puke that puts you in touch
with the universe but it'll make you
glow in the dark!

Date:
From: Martin Brown
Subject: Re: Positions with the most legal moves

Date: 13 Oct 2006 21:50:29
From:
Subject: Re: Positions with the most legal moves

Bob wrote:
>
> Thanks Fred, good to know I not crazy (or at least not alone ;)
>
> Do you have firm references to back this up? I have seem the suggestion
> for legal postions referred to by [email protected] for
>
> --Side without move is not in check.
> --Each side has a King.
> --No more material than can be created via normal pawn promotions.
> {i.e. (#Rooks>2)+(#Bishops>2)+(#Knights>2)+(#Queens>1)+ #Pawns<=8}
> --No pawns on the 1st or 8th ranks.
>
> computer programs and computer competitions but do not have a reference
> for the more logical standard definition. Any help putting a nail in
> this will be appreciated.

See Article 14 "Legality of Positions" at
<http://www.sci.fi/~stniekat/pccc/codex.htm >

Date: 13 Oct 2006 16:40:22
From:
Subject: Re: Positions with the most legal moves

>
> However, this is surely the longest tournament game played, and not the
> game containing the position with the largest number of legal moves for
> either black or white.

Yes sorry, i just have read very carelessly your original post....

Date: 13 Oct 2006 16:36:48
From:
Subject: Re: Positions with the most legal moves

=CE=9F/=CE=97 [email protected] =CE=AD=CE=B3=CF=81=CE=B1=CF=88=CE=B5:
> Bob wrote:
> > There is no definative algorithm to state whether a postion is legal. A
> > legal postion can only occur from a legal sequence of moves from the
> > starting postion.
>
> That's YOUR definition, and while it is valid it is certainly not the
> most commonly accepted one, which is:

What is a Chess position? It is a position that occurs in the game of
Chess(with legal moves, needless to say)!
That means positions that cannot occur in a game of Chess, are not
Chess positions. The fact that they "seem" normal should not confuse
us....

Of course it's a matter of taste and somewhat pointless so we should
not argue about that....

> -- Side to move is not in check.
> -- Each side has a King.
> -- No more material than can be created via normal pawn promotions.
> -- No pawns on the 1st or 8th ranks.

So these are legal for you? :-)

Hmm....Draw?
n6K/P6p/P1p2p2/P3p1np/PN1P3p/2P2P1p/P6p/k6N w - - 0 1
White wins?
b2K3b/1p4p1/2p2p2/3pp3/3PP3/2P2P2/1P4P1/B2k3B w - - 0 1
Is black better.....?
3QBRK1/3PPPNP/4PNRB/5PPP/ppp5/brnp4/pnppp3/1krbq3 w - - 0 1

For me they are not legal, so i save time by not analysing them, as i
ignore them....:-)

Date: 13 Oct 2006 15:57:45
From:
Subject: Re: Positions with the most legal moves

tin Brown wrote:
> Whilst I was watching Shredder dissect a position last night I got to
> wondering what was the legal position on a chess board that maximises
> the number of valid moves for white (to move).

Here are some records from Anthony Dickins' "A Guide to Fairy Chess",
2nd edition (1969); maybe some of these have been surpassed.

No promoted men, no promotion in play: 109 moves, W. Cross, 1967
5k2/2K5/3N1B1P/P1NB4/6Q1/4R3/P1PP1P1P1R6

No promoted men, with promotion in play: 144 moves, Dr. Jeno Ban, 1960
n1r1r1b1/1P1P1P1P/1Q6/3NBNK/R7/4p1p1/3PBPkP/2R5

With promoted men: 218 moves, A. S. M. Dickins, 1968
3Q4/1Q4Q1/4Q3/2Q4R/Q4Q2/3Q4/1Q4Rp/1K1BBNNk

Illegal position, 288 moves: N. Petrovic, 1946
BQQQQQQB/Q6Q/Q6Q/Q6Q/Q6Q/Q6Q/Q6Q/BQQQQQQB

All 32 men, 99 moves: H. H. Cross, 1946
q2Q3r/n6R/kpB1N1K1/p1p1Bppp/1RN3P1/1n1pp1b1/P1PPPP1P/r5Rb

Date: 13 Oct 2006 15:55:25
From:
Subject: Re: Positions with the most legal moves

The composition of Nenad Petrovic in 1964 holds the record of the most
possible legal moves with its 218 moves!

R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1

tin Brown wrote:
> Whilst I was watching Shredder dissect a position last night I got to
> wondering what was the legal position on a chess board that maximises
> the number of valid moves for white (to move).
>
> This problem comes in several flavours - all the major pieces RRNNBBQKk
> placed and a few pawns (promotions not allowed), and then any choice of
> pieces up to a maximum of 8 pawn promotions.
>
> The first try was to use all the major pieces and a few pawns (ignoring
> promotions).
>
> My initial solution based on the heuristic of placing all the pieces
> according to their mobility and avoiding any blocking and then adding
> pawns to taste is the following:
>
> 1R6/R7/5K1P/3Q4/5NB1/2N1P3/2B2P1P/6k1 w - - 0 1
>
> This generates 100 possible legal moves for white and places
> RRNNBBQKPPPPk
>
> I know the bishops are on the same colour but I couldn't get to the
> nice round 100 number without making that compromise. Perhaps someone
> else (or a program) can.
>
> I think the highest absolute mobility is somewhere above 190 based on
> an 8 queens configuration with kings placed at the edge of the board
> (best queens only I found so far was 157). I also found an apparently
> legal position in the process that appeared to break Shredder 10 (and
> other engines).
>
> 1K1k4/5Q2/7Q/1Q6/6Q1/Q7/2Q5/4Q3 w - - 0 1
>
> It works OK the first time, but fatally damages the engine so that the
> program needs restarting.
>
> Adding the spare 2Q and maybe 2R 2B will get a higher move count 191
> but the following position causes some engines to give up completely
> (although setup accepts it as valid)
>
> QK1k3B/5Q2/R6Q/1Q6/6Q1/Q6R/2Q5/Q3Q2B b - - 0 1
>
> The best I have so far using the 2N in addition has 194 valid moves:
>
> BKNkN2B/5Q2/R6Q/1Q6/6Q1/Q6R/2Q5/Q3Q2Q w - - 0 1
>
> Can anyone find a position to break through the 200 barrier?
>
> The final question which is a lot more tricky to answer is what is the
> position with the greatest number of legal moves for black or white
> that has ever been recorded in tournament play?
>
> I have a hunch that it is probably less than 64 but I could be wrong.
>
> Regards,
> tin Brown

Date: 13 Oct 2006 15:38:52
From:
Subject: Re: Positions with the most legal moves

[email protected] wrote:
> Bob wrote:
> > There is no definative algorithm to state whether a postion is legal. A
> > legal postion can only occur from a legal sequence of moves from the
> > starting postion.
>
> That's YOUR definition, and while it is valid it is certainly not the
> most commonly accepted one, which is:
> -- Side to move is not in check.
> -- Each side has a King.
> -- No more material than can be created via normal pawn promotions.
> -- No pawns on the 1st or 8th ranks.
>
> The reason for this is that, in computer chess, you should be able to
> drop any legal FEN into a chess engine to analyze the position. In this
> case, it doesn't matter how the position was arrived at.

Bob's definition is not HIS definition, it is the *standard* definition
of a legal position. Has been for well over 100 years. The fact that
chess engines should be able to accept some illegal positions is
irrelevant.

Date: 14 Oct 2006 01:32:37
From: Bob
Subject: Re: Positions with the most legal moves

[email protected] wrote:

> [email protected] wrote:
> > Bob wrote:
> > > There is no definative algorithm to state whether a postion is
> > > legal. A legal postion can only occur from a legal sequence of
> > > moves from the starting postion.
> >
> > That's YOUR definition, and while it is valid it is certainly not
> > the most commonly accepted one, which is:
> > -- Side to move is not in check.
> > -- Each side has a King.
> > -- No more material than can be created via normal pawn promotions.
> > -- No pawns on the 1st or 8th ranks.
> >
> > The reason for this is that, in computer chess, you should be able
> > to drop any legal FEN into a chess engine to analyze the position.
> > In this case, it doesn't matter how the position was arrived at.
>
> Bob's definition is not HIS definition, it is the standard definition
> of a legal position. Has been for well over 100 years. The fact that
> chess engines should be able to accept some illegal positions is
> irrelevant.

Thanks Fred, good to know I not crazy (or at least not alone ;)

Do you have firm references to back this up? I have seem the suggestion
for legal postions referred to by [email protected] for

--Side without move is not in check.
--Each side has a King.
--No more material than can be created via normal pawn promotions.
{i.e. (#Rooks >2)+(#Bishops>2)+(#Knights>2)+(#Queens>1)+ #Pawns<=8}
--No pawns on the 1st or 8th ranks.

computer programs and computer competitions but do not have a reference
for the more logical standard definition. Any help putting a nail in
this will be appreciated.

Bob

Date: 13 Oct 2006 23:55:18
From: Dave (from the UK)
Subject: Re: Positions with the most legal moves

[email protected] wrote:
> [email protected] wrote:
>
>>Bob wrote:
>>
>>>There is no definative algorithm to state whether a postion is legal. A
>>>legal postion can only occur from a legal sequence of moves from the
>>>starting postion.
>>
>>That's YOUR definition, and while it is valid it is certainly not the
>>most commonly accepted one, which is:
>>-- Side to move is not in check.
>>-- Each side has a King.
>>-- No more material than can be created via normal pawn promotions.
>>-- No pawns on the 1st or 8th ranks.
>>
>>The reason for this is that, in computer chess, you should be able to
>>drop any legal FEN into a chess engine to analyze the position. In this
>>case, it doesn't matter how the position was arrived at.
>
>
> Bob's definition is not HIS definition, it is the *standard* definition
> of a legal position. Has been for well over 100 years. The fact that
> chess engines should be able to accept some illegal positions is
> irrelevant.
>

Can someone explain the logic of "Side to move is not in check"? I can
play any old game and being in check and (hopefully) have multiple ways
of getting out of it.

More logical would be "The opponent of the side to move is not in check".
--
Dave (from the UK)

Please note my email address changes periodically to avoid spam.
It is always of the form: [email protected]
Hitting reply will work for a few months only - later set it manually.

http://witm.sourceforge.net/ (Web based Mathematica front end)

Date:
From: Martin Brown
Subject: Re: Positions with the most legal moves

Date: 13 Oct 2006 18:27:05
From: Gian-Carlo Pascutto
Subject: Re: Positions with the most legal moves

tin Brown wrote:
> Gian-Carlo Pascutto wrote:
>> tin Brown wrote:
>>
>>> The highest mobility position I spotted in that game was at
>>>
>>> r4bk1/pp1b2r1/3p1nqp/3Pp1n1/1PN1P3/P1NB1Q2/6PP/1RB1R2K w - - 0 28
>>>
>>> Where white has 47 legal moves.
>>>
>>> I am pretty sure that more open positions with active Q, R & B can get
>>> a fair bit higher than this But I haven't seen anything past 60 yet.
>>> Branching factors usually hover around 30+-10 for most serious games,
>>> but I am curious how large they can get in real tournament play.
>> This is the current record holder:
>>
>> Podhorzer - Palda, XVI Trebitsch-Turnier, Vienna 1933
>> 1.d4 d5 2.Nf3 Nf6 3.c4 e6 4.Nc3 c6 5.e3 Be7 6.Bd3 Nbd7 7.O-O O-O 8.Qe2
>> Qc7 9.e4 dxe4 10.Nxe4 Nxe4 11.Bxe4 Bf6 12.Re1 Re8 13.Ne5 g6 14.Bf4 Qb6
>> 15.Rad1 Qa5 16.Nxc6 Qxa2 17.Ra1 Qb3 18.Ra3 Qb6 19.c5 Nxc5 20.dxc5 Qxc5
>> 21.Rc1 Qb6 22.Ne5 Qd6 23.Qb5 Qf8 24.Ng4 Bg7 White has 75 moves here -
>> without promoted pieces and without promotion moves. After 25.Bd6 Re7
>> 26.Qc5 Black resigned.
>
> WOW! Thank you!!!
> How *did* you find that one ?

http://www.xs4all.nl/~timkr/chess2/diary_11.htm

See entry 212.

--
GCP

Date:
From: Martin Brown
Subject: Re: Positions with the most legal moves

Date: 13 Oct 2006 18:13:50
From: Bob
Subject: Re: Positions with the most legal moves

tin Brown wrote:

>
> Dave (from the UK) wrote:
> > [email protected] wrote:
> > > Bob wrote:
> > >
> > > > There is no definative algorithm to state whether a postion is
> > > > legal. A legal postion can only occur from a legal sequence of
> > > > moves from the starting postion.
>
> That is an excessively restrictive definition. There are plenty of
> good puzzle compositions that could not be reached by any sequence of
> legal chess moves. The position is still legal though and can be
> played forwards even if there is no possible prior move sequence to
> ge to it (ie in extremis it is a Garden of Eden position if there is
> no possible prior move at all).
>
> > > That's YOUR definition, and while it is valid it is certainly not
> > > the most commonly accepted one, which is:
> > > -- Side to move is not in check.
> >
> > Why is that in the definition? It seems very unreasonable.
>
> I suspect that is a typo for "side not to move is not in check"
> (a valid position should never leave the option king capture)
>
> > > -- Each side has a King.
> >
> > That's obvious.
> >
> > > -- No more material than can be created via normal pawn
> > > promotions.
> >
> > Reasonable.
> >
> > > -- No pawns on the 1st or 8th ranks.
> >
> > Makes sense.
> >
> > > The reason for this is that, in computer chess, you should be
> > > able to drop any legal FEN into a chess engine to analyze the
> > > position. In this case, it doesn't matter how the position was
> > > arrived at.
>
> Ditto for chess puzzles compositions which have a much longer
> history..
>
> Regards,
> tin Brown

Hi tin,

You seem to be replying to both Dave's post and Mine so I will reply
here.

If you wish i will distinguish "legal" positions from "possible"
postions. By possible postition I will mean those postions that could
be arrived out by a sequence of legal moves from the standard staring
postion. For legal postions I will defer to the (corrected) definition
mentioned by [email protected], i.e.

--Side without move is not in check.
--Each side has a King.
--No more material than can be created via normal pawn promotions.
(What is the simple rule for this? I don�t know what you mean by
normal pawn promotion.It implies a sequence of moves does it not?)
May I suggest that:
(#Rooks >2)+ (#Bishops>2)+ (#Knights>2)+ (#Queens>1)+ Pawns <= 8
Seems reasonable.
--No pawns on the 1st or 8th ranks.

Yes my definition of possible position is restrictive, but all rules
imply restriction. My defintion is implied by the rules of the game of
chess.

Puzzle compositions are a form of art in my opinion and as such have
carte blanche for challenging the rules. The humor and beauty that
result from ignoring rules is part of what makes art artistic. Also, I
am certain that there are puzzles that do not meet the "legal" postion
definition either.

Your original question however was more a mathematical question than an
artistic one. The counting of positions can only take place with an
agreed upon definition for which positions are allowed. By changing the
rules you can arrive at any number you wish -- in which case there is
little point in asking the question. However, I thought the the
question of finding such positions that are possible was a more
challenging and interesting question.

In my opinion the "legal" rules above were developed to weed out
non-possible positions for computer algorithms. They are not complete.
The criteria provide a necessary but not sufficient check for the
postion to be possible.

Here are a few more examples of "legal" but not "possible" positions.
rnbqkbnr/p6P/p6P/pp4PP/pp4PP/p6P/p6P/RNBQKBNR w KQkq - 0 1
rnbqkbnr/pppppppp/8/8/3Q4/8/PPPPPPPP/RNB1KBNR w KQkq - 0 1
rnbqkbnr/pppppppp/8/8/8/8/RNBQQBNR/RNBQKBNR w KQkq - 0 1
rnbqkb1r/ppp2ppp/3p1n2/3p4/3PP3/2P5/PP3PPP/RNBQKBNR w KQkq - 0 1
rnbqkbnr/pp1p1ppp/8/4P3/3Pp3/8/PPP2PPP/RNBQKBNR b KQkq - 0 1
rnbqk2r/pppp1p2/3bpnpp/8/3Q2P1/2N2P1P/PPPP4/RKB2BNR w kq - 0 1

Looking at these it is easy to see that improvements to the test
criteria could be made to furthur reduce the possiblity that a
non-possible position is deemed legal.

Bob

--

Date: 17 Oct 2006 21:06:45
From: David Richerby
Subject: Re: Positions with the most legal moves

Bob <[email protected] > wrote:
> Your original question however was more a mathematical question than
> an artistic one. The counting of positions can only take place with
> an agreed upon definition for which positions are allowed. By
> changing the rules you can arrive at any number you wish

Actually, that's not true. There can be no position with more than
32x27=864 possible moves because there can be at most 32 pieces on
the board and no piece can possibly have more than 27 legal moves (an
unobstructed queen on d4/d5/e4/e5).

(Well, OK, you could change the rules so that you can have more than
32 pieces, even more than one per square. And you could say that
moving the seventh queen on a1 to a2, then a3, then back to a1, then
to d7 is a move. So you could get an infinite number of moves from a
position but...)

Dave.

--
David Richerby Lead Windows (TM): it's like a
www.chiark.greenend.org.uk/~davidr/ graphical user interface that weighs
a ton!

Date: 13 Oct 2006 08:33:28
From:
Subject: Re: Positions with the most legal moves

Bob wrote:
> There is no definative algorithm to state whether a postion is legal. A
> legal postion can only occur from a legal sequence of moves from the
> starting postion.

That's YOUR definition, and while it is valid it is certainly not the
most commonly accepted one, which is:
-- Side to move is not in check.
-- Each side has a King.
-- No more material than can be created via normal pawn promotions.
-- No pawns on the 1st or 8th ranks.

The reason for this is that, in computer chess, you should be able to
drop any legal FEN into a chess engine to analyze the position. In this
case, it doesn't matter how the position was arrived at.

jm

Date: 13 Oct 2006 15:58:01
From: Bob
Subject: Re: Positions with the most legal moves

[email protected] wrote:

> Bob wrote:
> > There is no definative algorithm to state whether a postion is
> > legal. A legal postion can only occur from a legal sequence of
> > moves from the starting postion.
>
> That's YOUR definition, and while it is valid it is certainly not the
> most commonly accepted one, which is:
> -- Side to move is not in check.
> -- Each side has a King.
> -- No more material than can be created via normal pawn promotions.
> -- No pawns on the 1st or 8th ranks.
>
> The reason for this is that, in computer chess, you should be able to
> drop any legal FEN into a chess engine to analyze the position. In
> this case, it doesn't matter how the position was arrived at.
>
> jm

Hi JM,

Your right that is my definition. (I am not an a afficianado of all the
rules for all organizations but I believe a position resulting from an
illegal game is an illegal position.)

I would assert that because something is held commonly does not make it
correct. One must examine the reasons for the widely held perception.

A computer algorithm must check for illegality to prune its tree.
Because of that, a simple alogorythm is used to definatively state
positions that are not legal.

However, failing to be rejected by someone's definition of illegality
does not make the position legal. In this case it simply means that no
one has found a better algorithm to test legality (as far as I know).

The alternate definition of a legal position is held because it is
simpler not because it is correct -- IMHO.

Bob
--

Date: 13 Oct 2006 16:37:34
From: Dave (from the UK)
Subject: Re: Positions with the most legal moves

[email protected] wrote:
> Bob wrote:
>
>>There is no definative algorithm to state whether a postion is legal. A
>>legal postion can only occur from a legal sequence of moves from the
>>starting postion.
>
>
> That's YOUR definition, and while it is valid it is certainly not the
> most commonly accepted one, which is:
> -- Side to move is not in check.

Why is that in the definition? It seems very unreasonable.

> -- Each side has a King.

That's obvious.

> -- No more material than can be created via normal pawn promotions.

Reasonable.

> -- No pawns on the 1st or 8th ranks.

Makes sense.

> The reason for this is that, in computer chess, you should be able to
> drop any legal FEN into a chess engine to analyze the position. In this
> case, it doesn't matter how the position was arrived at.
>
> jm
>

--
Dave (from the UK)

Please note my email address changes periodically to avoid spam.
It is always of the form: [email protected]
Hitting reply will work for a few months only - later set it manually.

http://witm.sourceforge.net/ (Web based Mathematica front end)

Date:
From: Martin Brown
Subject: Re: Positions with the most legal moves

Date: 13 Oct 2006 16:20:42
From: Gian-Carlo Pascutto
Subject: Re: Positions with the most legal moves

tin Brown wrote:

> The highest mobility position I spotted in that game was at
>
> r4bk1/pp1b2r1/3p1nqp/3Pp1n1/1PN1P3/P1NB1Q2/6PP/1RB1R2K w - - 0 28
>
> Where white has 47 legal moves.
>
> I am pretty sure that more open positions with active Q, R & B can get
> a fair bit higher than this But I haven't seen anything past 60 yet.
> Branching factors usually hover around 30+-10 for most serious games,
> but I am curious how large they can get in real tournament play.

This is the current record holder:

Podhorzer - Palda, XVI Trebitsch-Turnier, Vienna 1933
1.d4 d5 2.Nf3 Nf6 3.c4 e6 4.Nc3 c6 5.e3 Be7 6.Bd3 Nbd7 7.O-O O-O 8.Qe2
Qc7 9.e4 dxe4 10.Nxe4 Nxe4 11.Bxe4 Bf6 12.Re1 Re8 13.Ne5 g6 14.Bf4 Qb6
15.Rad1 Qa5 16.Nxc6 Qxa2 17.Ra1 Qb3 18.Ra3 Qb6 19.c5 Nxc5 20.dxc5 Qxc5
21.Rc1 Qb6 22.Ne5 Qd6 23.Qb5 Qf8 24.Ng4 Bg7 White has 75 moves here -
without promoted pieces and without promotion moves. After 25.Bd6 Re7
26.Qc5 Black resigned.

--
GCP

Date: 13 Oct 2006 14:19:25
From: Bob
Subject: Re: Positions with the most legal moves

tin Brown wrote:

>
> [email protected] wrote:
> > > The best I have so far using the 2N in addition has 194 valid
> > > moves:
> > >
> > > BKNkN2B/5Q2/R6Q/1Q6/6Q1/Q6R/2Q5/Q3Q2Q w - - 0 1
> >
> > This position is not legal!
>
> How so? Kings are not in check and there are 9xQ, RR,NN,BB placed.
> (it was cut & pasted from the Shredder board)
>

There is no definative algorithm to state whether a postion is legal. A
legal postion can only occur from a legal sequence of moves from the
starting postion.

Your posted position is illegal because there is no legal move for
black to have made to get into it. Your position can only be arrived at
if white moved while black was in check.

> > > Can anyone find a position to break through the 200 barrier?
> >
> > 218 moves available in the:
> > R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1
>

In this postion blacks last move had to have been b2.

In itself this doesn't mean the position is legal either. The only way
to prove it was legal is to generate a legal sequence of moves to get
to this positon.

In this case it is still possible that this can NOT be done. I have
managed to backtrack about 8 moves and have started from the original
position to get the close but have not found a sequence of moves to
arrive at this postion yet.
For example:

1. e4 f5 2. d4 e5 3. c4 d5 4. b4 c5 5. bxc5 Bd7 6. cxd5 Ba4 7. dxe5 Bb3
8.
axb3 Nc6 9. exf5 Na5 10. Ba3 Nc4 11. bxc4 Qg5 12. Nf3 g6 13. Nxg5 Ne7
14.
fxg6 Ng8 15. gxh7 Rb8 16. hxg8=Q Ra8 17. Qxh8 Kd7 18. Qxf8 Kc7 19. Qxa8
Kd7
20. h4 Kc7 21. h5 Kd7 22. h6 Kc7 23. h7 Kd7 24. h8=Q Kc7 25. Nf7 Kd7
26. g3
Kc7 27. g4 Kd7 28. g5 Kc7 29. g6 Kd7 30. g7 Kc7 31. g8=Q Kd7 32. e6+ Kc7
33. e7 Kd7 34. e8=Q+ Kc7 35. Qef8 Kd7 36. Qg1 Kc7 37. Qb2 Kd7 38. Qh6
Kc7
39. Qhc1 Kd7 40. Ng5 Kc7 41. f4 Kd7 42. f5 Kc7 43. f6 Kd7 44. f7 Kc7 45.
f8=Q Kd7 46. Qff2 Kc7 47. Qdb3 Kd7 48. d6 Kc6 49. d7 Kc7 50. d8=Q+ Kc6
51.
Qdd1 Kc7 52. Qdc2 Kd7 53. Nf3 Ke7 54. c6+ Kf7 55. c7 Ke6 56. c8=Q+ Kf7
57.
Qcc5 Ke6 58. Qcb4 Kf7 59. c5+ Ke7 60. Qbd3 Kf7 61. Nc3 Kf6 62. Bg2 Kg7
63.
c6 Kf6 64. c7 Kg7 65. c8=Q Kf6 66. Ke2 Kg7 67. Qcb8 Kf6 68. Qdd1 Kf7 69.
Kd3 Ke6 70. Qbb1 Kf7 71. Q4b2 Ke6 72. Qh4 Kf7 73. Rh3 Ke6 74. Qgh2 Kf7
75.
Qdh1 Ke6 76. Qcf2 Kf7 77. Qcg1 Ke6 78. Qbf1 Kf7 79. Ne2 Ke6 80. Qbc1 Kf7
81. Qce1 Ke6 82. Rd1 Kd5 83. Bc5 Kc6 84. Bd4 Kb5

etcetera??

Clearly I have too much time on my hands.
Take care,
Bob

> Pretty good! Any advance on 218?
>
> > > The final question which is a lot more tricky to answer is what
> > > is the position with the greatest number of legal moves for black
> > > or white that has ever been recorded in tournament play?
> >
> > It was in 1989 between I.Nikolic and Arsovic and it was 269
> > moves!!!!!!!!
> > They were playing for 20 hours and 15 minutes!
>
> No wonder he missed the mate in 5 on move 201 then!
>
> 201 Rg7 ? but
> 201 Rf3 Rd2 202 Rb3 Kf8 203 Rg3 Rg2 204 Bxg2 205 Kd8 Rb8#
>
> White was particularly unlucky with Rg7? in this game
> 64. Rg7? robbed him of near certain victory much earlier on.
>
> However, this is surely the longest tournament game played, and not
> the game containing the position with the largest number of legal
> moves for either black or white.
>
> The highest mobility position I spotted in that game was at
>
> r4bk1/pp1b2r1/3p1nqp/3Pp1n1/1PN1P3/P1NB1Q2/6PP/1RB1R2K w - - 0 28
>
> Where white has 47 legal moves.
>
> I am pretty sure that more open positions with active Q, R & B can get
> a fair bit higher than this But I haven't seen anything past 60 yet.
> Branching factors usually hover around 30+-10 for most serious games,
> but I am curious how large they can get in real tournament play.
>
> Regards,
> tin Brown

--

Date: 13 Oct 2006 14:38:17
From: Bob
Subject: Re: Positions with the most legal moves

Here is proof that the position posted by [email protected] is legal:

1. e4 f5 2. d4 e5 3. c4 d5 4. b4 c5 5. bxc5 Bd7 6. cxd5 Ba4 7. dxe5 Bb3
8.
axb3 Nc6 9. exf5 Na5 10. Ba3 Nc4 11. bxc4 Qg5 12. Nf3 g6 13. Nxg5 Ne7
14.
fxg6 Ng8 15. gxh7 Rb8 16. hxg8=Q Ra8 17. Qxh8 Kd7 18. Qxf8 Kc7 19. Qxa8
Kd7
20. h4 Kc7 21. h5 Kd7 22. h6 Kc7 23. h7 Kd7 24. h8=Q Kc7 25. Nf7 Kd7
26. g3
Kc7 27. g4 Kd7 28. g5 Kc7 29. g6 Kd7 30. g7 Kc7 31. g8=Q Kd7 32. e6+ Kc7
33. e7 Kd7 34. e8=Q+ Kc7 35. Qef8 Kd7 36. Qg1 Kc7 37. Qb2 Kd7 38. Qh6
Kc7
39. Qhc1 Kd7 40. Ng5 Kc7 41. f4 Kd7 42. f5 Kc7 43. f6 Kd7 44. f7 Kc7 45.
f8=Q Kd7 46. Qff2 Kc7 47. Qdb3 Kd7 48. d6 Kc6 49. d7 Kc7 50. d8=Q+ Kc6
51.
Qdd1 Kc7 52. Qdc2 Kd7 53. Nf3 Ke7 54. c6+ Kf7 55. c7 Ke6 56. c8=Q+ Kf7
57.
Qcc5 Ke6 58. Qcb4 Kf7 59. c5+ Ke7 60. Qbd3 Kf7 61. Nc3 Kf6 62. Bg2 Kg7
63.
c6 Kf6 64. c7 Kg7 65. c8=Q Kf6 66. Ke2 Kg7 67. Qcb8 Kf6 68. Qdd1 Kf7 69.
Kd3 Ke6 70. Qbb1 Kf7 71. Q4b2 Ke6 72. Qh4 Kf7 73. Rh3 Ke6 74. Qgh2 Kf7
75.
Qdh1 Ke6 76. Qcf2 Kf7 77. Qcg1 Ke6 78. Qbf1 Kf7 79. Ne2 Ke6 80. Qbc1 Kf7
81. Qce1 Ke6 82. Rd1 Kd5 83. Bc5 Kc6 84. Bd4 Kb5 85. Nc1 Ka4 86. Nd2 Ka3
87. Qhd8 a6 88. Qba7 b6 89. Q8b7 Ka4 90. Rh8 Ka3 91. Ne2 Ka2 92. Qdd7
Ka3
93. Ra8 Ka2 94. Qh5 Ka3 95. Qhe8 Ka2 96. Qg3 b5 97. Qgb8 Ka3 98. Qbb6
Ka2
99. Qeg3 Ka3 100. Nf4 Ka2 101. Re1 Ka3 102. Re7 Ka2 103. Rh7 Ka3 104.
Rh8
Ka2 105. Qg1h2 Ka3 106. Bg1 Ka2 107. Bd5+ Ka3 108. Qfe2 Kb2 109. Qhh4
Ka1
110. Qhf3 Kb2 111. Bf7 Ka1 112. Nd5 Kb2 113. Ke3 Ka1 114. Kf2 Kb2 115.
Kf1
Ka1 116. Nb3+ Kb1 117. Nc1 Ka1 118. Qhf4 Kb1 119. Qgh4 Ka1 120. Qed2 Kb1
121. Q4e4+ Ka1 122. Qc4 Kb1 123. Bg6+ Ka1 124. Nc3 a5 125. Bb1 b4 126.
Qbe5
a4 127. Qeg6 a3 128. Qaa4 a2 129. Qa3 b3 130. Nd1+ b2
*
--

Date: 13 Oct 2006 05:06:52
From:
Subject: Re: Positions with the most legal moves

> The best I have so far using the 2N in addition has 194 valid moves:
>
> BKNkN2B/5Q2/R6Q/1Q6/6Q1/Q6R/2Q5/Q3Q2Q w - - 0 1

This position is not legal!

>
> Can anyone find a position to break through the 200 barrier?

218 moves available in the:
R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1

>
> The final question which is a lot more tricky to answer is what is the
> position with the greatest number of legal moves for black or white
> that has ever been recorded in tournament play?

It was in 1989 between I.Nikolic and Arsovic and it was 269
moves!!!!!!!!
They were playing for 20 hours and 15 minutes!

[Event "Belgrade"]
[Site "Belgrade"]
[Date "1989.??.??"]
[Round "?"]
[White "Nikolic, I."]
[Black "Arsovic"]
[Result "1/2-1/2"]
[ECO "E95"]
[PlyCount "538"]
[EventDate "1989.??.??"]

1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. Nf3 O-O 6. Be2 Nbd7 7. O-O e5
8. Re1
Re8 9. Bf1 h6 10. d5 Nh7 11. Rb1 f5 12. Nd2 f4 13. b4 g5 14. Nb3 Bf8
15. Be2
Ndf6 16. c5 g4 17. cxd6 cxd6 18. a3 Ng5 19. Bf1 Re7 20. Qd3 Rg7 21. Kh1
Qe8 22.
Nd2 g3 23. fxg3 fxg3 24. Qxg3 Nh3 25. Qf3 Qg6 26. Nc4 Bd7 27. Bd3 Ng5
28. Bxg5
Qxg5 29. Ne3 Re8 30. Ne2 Be7 31. Rbd1 Rf8 32. Nf5 Ng4 33. Neg3 h5 34.
Kg1 h4
35. Qxg4 Qxg4 36. Nh6+ Kh7 37. Nxg4 hxg3 38. Ne3 gxh2+ 39. Kxh2 Rh8 40.
Rh1
Kg6+ 41. Kg1 Rc8 42. Be2 Rc3 43. Rd3 Rc1+ 44. Nf1 Bd8 45. Rh8 Bb6+ 46.
Kh2 Rh7+
47. Rxh7 Kxh7 48. Nd2 Bg1+ 49. Kh1 Bd4+ 50. Nf1 Bg4 51. Bxg4 Rxf1+ 52.
Kh2 Bg1+
53. Kh3 Re1 54. Bf5+ Kh6 55. Kg4 Re3 56. Rd1 Bh2 57. Rh1 Rg3+ 58. Kh4
Rxg2 59.
Kh3 Rg3+ 60. Kxh2 Rxa3 61. Rg1 Ra6 62. Rg6+ Kh5 63. Kg3 Rb6 64. Rg7
Rxb4 65.
Bc8 a5 66. Bxb7 a4 67. Bc6 a3 68. Ra7 Rb3+ 69. Kf2 Kg5 70. Ke2 Kf4 71.
Ra4 Rh3
72. Kd2 a2 73. Bb5 Rh1 74. Rxa2 Rh2+ 75. Be2 Kxe4 76. Ra5 Kd4 77. Ke1
Rh1+ 78.
Kf2 Rc1 79. Bg4 Rc2+ 80. Ke1 e4 81. Be6 Ke5 82. Bg8 Rc8 83. Bf7 Rc7 84.
Be6 Rc2
85. Ra8 Rb2 86. Ra6 Rg2 87. Kd1 Rb2 88. Ra5 Rg2 89. Bd7 Rh2 90. Bc6 Kf4
91. Ra8
e3 92. Re8 Kf3 93. Rf8+ Ke4 94. Rf6 Kd3 95. Bb5+ Kd4 96. Rf5 Rh1+ 97.
Ke2 Rh2+
98. Kd1 Rh1+ 99. Kc2 Rh2+ 100. Kc1 Rh1+ 101. Kc2 Rh2+ 102. Kd1 Rh1+
103. Ke2
Rh2+ 104. Kf1 Rb2 105. Be2 Ke4 106. Rh5 Rb1+ 107. Kg2 Rb2 108. Rh4+
Kxd5 109.
Kf3 Kc5 110. Kxe3 Rb3+ 111. Bd3 d5 112. Rh8 Ra3 113. Re8 Kd6 114. Kd4
Ra4+ 115.
Kc3 Ra3+ 116. Kd4 Ra4+ 117. Ke3 Ra3 118. Rh8 Ke5 119. Rh5+ Kd6 120. Rg5
Rb3
121. Kd2 Rb8 122. Bf1 Re8 123. Kd3 Re5 124. Rg8 Rh5 125. Bg2 Kc5 126.
Rf8 Rh6
127. Bf3 Rd6 128. Re8 Rc6 129. Ra8 Rb6 130. Rd8 Rd6 131. Rf8 Ra6 132.
Rf5 Rd6
133. Kc3 Rd8 134. Rg5 Rd6 135. Rh5 Rd8 136. Rf5 Rd6 137. Rf8 Ra6 138.
Re8 Rc6
139. Ra8 Rb6 140. Ra5+ Rb5 141. Ra1 Rb8 142. Rd1 Rd8 143. Rd2 Rd7 144.
Bg2 Rd8
145. Kd3 Ra8 146. Ke3 Re8+ 147. Kd3 Ra8 148. Kc3 Rd8 149. Bf3 Rd7 150.
Kd3 Ra7
151. Bg2 Ra8 152. Rc2+ Kd6 153. Rc3 Ra2 154. Bf3 Ra8 155. Rb3 Ra5 156.
Ke3 Ke5
157. Rd3 Rb5 158. Kd2 Rc5 159. Bg2 Ra5 160. Bf3 Rc5 161. Bd1 Rc8 162.
Bb3 Rc5
163. Rh3 Kf4 164. Kd3 Ke5 165. Rh5+ Kf4 166. Kd4 Rb5 167. Bxd5 Rb4+
168. Bc4
Ra4 169. Rh7 Kg5 170. Rf7 Kg6 171. Rf1 Kg5 172. Kc5 Ra5+ 173. Kc6 Ra4
174. Bd5
Rf4 175. Re1 Rf6+ 176. Kc5 Rf5 177. Kd4 Kf6 178. Re6+ Kg5 179. Be4 Rf6
180. Re8
Kf4 181. Rh8 Rd6+ 182. Bd5 Rf6 183. Rh1 Kf5 184. Be4+ Ke6 185. Ra1 Kd6
186. Ra5
Re6 187. Bf5 Re1 188. Ra6+ Ke7 189. Be4 Rc1 190. Ke5 Rc5+ 191. Bd5 Rc7
192. Rg6
Rd7 193. Rh6 Kd8 194. Be6 Rd2 195. Rh7 Ke8 196. Kf6 Kd8 197. Ke5 Rd1
198. Bd5
Ke8 199. Kd6 Kf8 200. Rf7+ Ke8 201. Rg7 Rf1 202. Rg8+ Rf8 203. Rg7 Rf6+
204.
Be6 Rf2 205. Bd5 Rf6+ 206. Ke5 Rf1 207. Kd6 Rf6+ 208. Be6 Rf2 209. Ra7
Kf8 210.
Rc7 Rd2+ 211. Ke5 Ke8 212. Kf6 Rf2+ 213. Bf5 Rd2 214. Rc1 Rd6+ 215. Be6
Rd2
216. Rh1 Kd8 217. Rh7 Rd1 218. Rg7 Rd2 219. Rg8+ Kc7 220. Rc8+ Kb6 221.
Ke5 Kb7
222. Rc3 Kb6 223. Bd5 Rh2 224. Kd6 Rh6+ 225. Be6 Rh5 226. Ra3 Ra5 227.
Rg3 Rh5
228. Rg2 Ka5 229. Rg3 Kb6 230. Rg4 Rb5 231. Bd5 Rc5 232. Rg8 Rc2 233.
Rb8+ Ka5
234. Bb3 Rc3 235. Kd5 Rc7 236. Kd4 Rd7+ 237. Bd5 Re7 238. Rb2 Re8 239.
Rb7 Ka6
240. Rb1 Ka5 241. Bc4 Rd8+ 242. Kc3 Rh8 243. Rb5+ Ka4 244. Rb6 Rh3+
245. Bd3
Rh5 246. Re6 Rg5 247. Rh6 Rc5+ 248. Bc4 Rg5 249. Ra6+ Ra5 250. Rh6 Rg5
251. Rh4
Ka5 252. Rh2 Rg3+ 253. Kd4 Rg5 254. Bd5 Ka4 255. Kc5 Rg3 256. Ra2+ Ra3
257. Rb2
Rg3 258. Rh2 Rc3+ 259. Bc4 Rg3 260. Rb2 Rg5+ 261. Bd5 Rg3 262. Rh2 Rc3+
263.
Bc4 Rg3 264. Rh8 Ka3 265. Ra8+ Kb2 266. Ra2+ Kb1 267. Rf2 Kc1 268. Kd4
Kd1 269.
Bd3 Rg7 1/2-1/2

>
> I have a hunch that it is probably less than 64 but I could be wrong.
>
> Regards,
> tin Brown

Date: 16 Oct 2006 12:32:23
From: Simon Krahnke
Subject: Re: Positions with the most legal moves

* Bob <[email protected] > (2006-10-14) schrieb:

>> But if you allow a game of chess from an alternate starting position,
>> restricting these positions to the ones that can be reached from the
>> standard starting position simply doesn't make sense.

> Sure we could talk about legal postions for tank chess, mini chess,
> Fisher chess, modern chess, 3d chess, and bughouse too -- but we
> weren't.

Yeah, I was talking about chess with an alternate starting position. No
change in catstling rules, no dropping of pieces. Only specifyng the
starting position with something like FEN.

Ant his is exactly what a normal chess engine will let you do.

> As I said in an earlier post, if you change the rules the number of
> legal positions would obviously change and you could make the answer to
> the original question whatever you desire.

That's right.

mfg, simon .... l

Date: 14 Oct 2006 09:20:04
From: Simon Krahnke
Subject: Re: Positions with the most legal moves

* Bob <[email protected] > (03:32) schrieb:

Obviosly not all these rules are equally important:

> --Side without move is not in check.
> --Each side has a King.
> --No pawns on the 1st or 8th ranks.

These basic rules ensure that can play chess according to its rules.

> --No more material than can be created via normal pawn promotions.
> {i.e. (#Rooks>2)+(#Bishops>2)+(#Knights>2)+(#Queens>1)+ #Pawns<=8}

But you could follow the rules if that was not ensured. Take a board
full of queens, with the kings far apart. If the queens are all of the
color that's not to move, it's just mate.

This makes the board look more realistic and limits the amount of
material in way that some chess engines might appreciate.

But if you allow a game of chess from an alternate starting position,
restricting these positions to the ones that can be reached from the
standard starting position simply doesn't make sense.

mfg, simon .... l

Date: 14 Oct 2006 21:24:04
From: Bob
Subject: Re: Positions with the most legal moves

Simon Krahnke wrote:

> * Bob <[email protected]> (03:32) schrieb:
>
> Obviosly not all these rules are equally important:
>
> > --Side without move is not in check.
> > --Each side has a King.
> > --No pawns on the 1st or 8th ranks.
>
> These basic rules ensure that can play chess according to its rules.
>
> > --No more material than can be created via normal pawn promotions.
> > {i.e. (#Rooks>2)+(#Bishops>2)+(#Knights>2)+(#Queens>1)+ #Pawns<=8}
>
> But you could follow the rules if that was not ensured. Take a board
> full of queens, with the kings far apart. If the queens are all of the
> color that's not to move, it's just mate.
>
> This makes the board look more realistic and limits the amount of
> material in way that some chess engines might appreciate.
>
> But if you allow a game of chess from an alternate starting position,
> restricting these positions to the ones that can be reached from the
> standard starting position simply doesn't make sense.
>
> mfg, simon .... l

Sure we could talk about legal postions for tank chess, mini chess,
Fisher chess, modern chess, 3d chess, and bughouse too -- but we
weren't.

As I said in an earlier post, if you change the rules the number of
legal positions would obviously change and you could make the answer to
the original question whatever you desire.

For standard chess, I stand by my answer.
Bob
--

Date: 13 Oct 2006 04:59:26
From: Sanny
Subject: very difficult problem

It is very difficult Problem

Bye
Sanny

Play Chess at: http://www.GetClub.com/Chess.html

Date:
From: Martin Brown
Subject: Re: Positions with the most legal moves