I think the exercise was to enumerate the set of possible move notations irrespective of what preceded or followed the move. In that context, the peice that previously occupied the spot the pawn is moving to (on the second or seventh rank) is irrelevant.
Number of Possible Chess Configurations
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RetGuvvie98 wrote:
but: in order for any pawn to reach a 'second rank' e.g. b2 or b7, there must be something missing off the board - as every pawn is blocked by an opposing pawn in the initial position - and when something is captured, --- DEPENDING ON WHAT IS CAPTURED --- the number of possible moves remaining will be drastically reduced by some number - quite variable and impossible to quantify with a formula that actually accounts for the variability in a rational sense.
You did not mention that reduction in your formula - making your formula invalid in the extreme because you have credited BOTH SIDES with potential to move all pawns to the enemy second rank (their own seventh rank) and that is physically impossible.
Now that I mention it, that feature alone renders this an irrational exercise by those who have time on their hands. the reduction in remaining possible moves or positions depends entirely on exactly what is captured and how many pawns remain after exchanges occur.
applying rational thought to the irrational babblings.
My calculations were not "invalid in the extreme" just because they don't answer the question you are interested in. I never stipulated or intended the count to be limited to one game. It was intended to be a count of the possible moves in all possible games, "move" being defined as a move with a distinct expression in algebraic notation. I think the first sentence of my post was pretty clear about that.
Please work on your "rational thought."
Feb 8, 2009
0
#64
rickyk586 wrote:
I'm not sure if this is the right place to post the question.
How many ACTUAL chess board configurations are their? I HAVE been able to find sites with answers to this question that include boards with extra pieces (like a board full of white Kings)
...................
actual board configurations - as stated above in the initial posting - - implies legally achievable inherently in the conceptualization. but all that is irrelevant if one (as some postings have postulated) allows permutations of positions where pawns have actually 'passed' other pawns without capturing anything, and then the hypothetical (non-realistic fantasy) engages in fantasyland musings, rather than realistic chess.
Thank you for the non sequitur.
hmmm, quite a lot of chat about this interesting subject, I will get my chess board out right now and work out every single possible position, I will post the answer as soon as humanly possible, then when everyone knows the correct answer, we can all relax!!! don't worry guys, I'm doing it for the team!!!
Feb 9, 2009
0
#67
A quick summary of the questions posed and the numbers supplied, for new-comers to the discussion ...
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How many ACTUAL chess board configurations are there? No extra pieces – but can include impossible-to-reach positions (Ricky586) |
1050 distinct board positions (artfizz) |
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1055 (elcabesa) |
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The game tree complexity? - which is all possible positions (Eniamar) |
10120 Shannon's number (Eniamar) |
|
the average chess game length (Eniamar) |
80 (Eniamar) |
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Board positions with 32 pieces? (cuendillar) |
1042 (cuendillar) |
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number of legal positions with JUST 2 KINGS on the board? (artfizz) |
3,612 (ichabod801) |
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possible legal positions with just a King and pawn vs. king endgame? (pvcmike) |
168,024 (pvcmike) |
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|
334,496 or 167,248. (ichabod801) |
|
Chess ( RetGuvvie98) |
|
|
possible chess games?.... (Sleeper) |
22600 (Sleeper) |
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The number of possible moves, recorded in short algebraic? (artfizz) |
~2,000 (artfizz) |
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17,306 (ichabod801) |
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45,586 (ichabod801) |
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longest single move in short algebraic notation? (artfizz) |
6 characters? (artfizz) |
|
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Nf3xd4++ [8 characters] (ichabod801) |
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ways to choose a set of Chess men from a standard set, if that set must include at least the two kings? (ichabod801) |
236,196 (ichabod801) |
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total of possible moves in a game of chess? (GuyOnTheCouch) |
10 to the power of (10 to the 50th) ( GuyOnTheCouch) |
Feb 9, 2009
0
#68
AWARDS FOR HIGHEST Number of responses:
FIRST/Second PLACE: Tie between: artfizz and ichabod801 - 7
third place to: Eniamar - 4
honorable mention to: cuendillar, GuyOnTheCouch, pvcmike, and last: Sleeper. with 2 each.
all others: honorable mention,
and
thanks for reading to the rest.
a gazillion!
I know I already plugged it earlier, but there is also some discussion here about the longest possible game:
I came to a ceiling of 5900 with some certainty that it is less than that. Revan24 arrived at 5870.5, although I'm not sure exactly how as I've not seen his calculations, I arrived at 5897.5 (the means by which I discounted half-tempos from the ceiling leaving a lot of opportunity for error).
Any other thoughts on that one?
Feb 9, 2009
0
#71
TheGrobe wrote:
I know I already plugged it earlier, but there is also some discussion here about ...
It appears the URL has gone AWOL. Could you possibly supply it again?
artfizz wrote:
TheGrobe wrote:
I know I already plugged it earlier, but there is also some discussion here about ...
It appears the URL has gone AWOL. Could you possibly supply it again?
Hmmm, I don't know why it dissapeared, and why it now won't let me update the original comment with it.... In any case, here is the link:
OK, that's just weird -- something must currently be wrong with the posting of URLs. Perhaps deliberately disabled for some reason (spam)?
Look at comment #60 as it has the link intact.
Feb 9, 2009
0
#74
TheGrobe wrote:
artfizz wrote:
TheGrobe wrote:
I know I already plugged it earlier, but there is also some discussion here about ...
It appears the URL has gone AWOL. Could you possibly supply it again? http://blog.chess.com/kurtgodden/the-longest-possible-chess-game-revisited
Hmmm, I don't know why it dissapeared, and why it now won't let me update the original comment with it.... In any case, here is the link:
The missing URL problem? ... described here ... http://www.chess.com/forum/view/help-support/little-problem-with-the-articles and here ... http://www.chess.com/forum/view/community/tally-forum-annoyances (post #53)
Feb 9, 2009
0
#75
TheGrobe wrote:
I know I already plugged it earlier, but there is also some discussion here about the longest possible game: http://blog.chess.com/kurtgodden/the-longest-possible-chess-game-revisited
I came to a ceiling of 5900 with some certainty that it is less than that. Revan24 arrived at 5870.5, although I'm not sure exactly how as I've not seen his calculations, I arrived at 5897.5 (the means by which I discounted half-tempos from the ceiling leaving a lot of opportunity for error).
Any other thoughts on that one?
Quick point for clarification: does a promotion count as a capture under the 50-move rule?
artfizz wrote:
TheGrobe wrote:
I know I already plugged it earlier, but there is also some discussion here about the longest possible game: http://blog.chess.com/kurtgodden/the-longest-possible-chess-game-revisited
I came to a ceiling of 5900 with some certainty that it is less than that. Revan24 arrived at 5870.5, although I'm not sure exactly how as I've not seen his calculations, I arrived at 5897.5 (the means by which I discounted half-tempos from the ceiling leaving a lot of opportunity for error).
Any other thoughts on that one?
Quick point for clarification: does a promotion count as a capture under the 50-move rule?
That doesn't matter, since it certainly counts as a pawn move.
Here's any easy one (or four): king and piece vs. king is 447,888. It's just 3,612 x 62 x 2, since you don't have to worry about things you have to worry about with pawns; such as they can only be in certain places, and can't even check from all of those.
Feb 9, 2009
0
#78
RetGuvvie98 wrote:
artfizz wrote:
cuendillar wrote:
Under those stipulations the problem isn't all that hard. For all 32 pieces it is 63!/(32!*8!*8!)=4.63*10^42 unless I've made a mistake in the calculations. The rest will take a little longer to work out but I'm working on it. My number is lower than the others as I've took into account that all pieces aren't different.
PS: 63 is not a typo.
It's a lot harder than you might think to count LEGAL positions. With 32 pieces, your calculations can make sure the right set of pieces is on the board i.e. 2 kings, 16 pawns, etc. However, there are a number of additional constraints such as: two kings must not occupy adjacent squares; white pawns cannot occupy the 'a' rank.
good point, Artfizz, but also, don't forget, while you cannot place two kings on adjacent squares; since you cannot place a king where it can be captured by any other piece, that will significantly reduce the remaining possible positions as well.
I suspect that those who establish calculations for 'maximum' number of positions ignore those stipulations and just look at physically possible positions, not the number of possible "legal chess" positions.
I am sure this has been pointed out, but placing the king where it can be captured is a legal position. Checks occur all the time, and checkmates, or conculsions to the game are important mathematically in the study of game theory. Those positions must be included.
Provided it's the player who's in check to move. I think that was the point, because two identical board configurations can actually be different positions depending on who's move it is, castling and en passant rights, how far down the 50 move rule you are and the distinct set all of the previous positions since (and their counts since):
- The last pawn move including the capture of a pawn
- The last castle
- Either side had more peices (not pawns) that they've since lost than they now have pawns
(All of the latter because of the threefold repetition rule).
To Answer the question how many configurations the board can be in, consider each configuration a State of the Board.
The Board has 10^120 States
This is every orientation of every posible move counter move and checkmate the game can have for either colour.
There are no stupid configurations like 2 pieces on one square or configurations with no kings that would be dumb.
ichabod801, pawns can't move to the first or second rank so there are 5 pawn moves, not including promotion, per pawn not 6.
No, black pawns can move to the second rank, but not the seventh. White pawns can move to the seventh rank but not the second. So "b2" and "b7" are both valid pawn moves, even if they are each only valid for one color.
but: in order for any pawn to reach a 'second rank' e.g. b2 or b7, there must be something missing off the board - as every pawn is blocked by an opposing pawn in the initial position - and when something is captured, --- DEPENDING ON WHAT IS CAPTURED --- the number of possible moves remaining will be drastically reduced by some number - quite variable and impossible to quantify with a formula that actually accounts for the variability in a rational sense.
You did not mention that reduction in your formula - making your formula invalid in the extreme because you have credited BOTH SIDES with potential to move all pawns to the enemy second rank (their own seventh rank) and that is physically impossible.
Now that I mention it, that feature alone renders this an irrational exercise by those who have time on their hands. the reduction in remaining possible moves or positions depends entirely on exactly what is captured and how many pawns remain after exchanges occur.
applying rational thought to the irrational babblings.