I'm sadly disappointed that possible promotions are not taken into account for this exercise. The title of the thread is an out-and-out lie.
I'll be back later...a female is paying attention to me...
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.
It appears the URL has gone AWOL. Could you possibly supply it again? http://blog.chess.com/kurtgodden/the-longest-possible-chess-game-revisited
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)
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.
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):
(All of the latter because of the threefold repetition rule).
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