In the chess moves thread, it was mentioned that a chess game could go on forever and various rules were mentioned about how to prevent that. Now, when I was playing chess, the only rule I knew of was that if the same sequence of moves had been made 3 times in a row, that would count as a stalemate and the game would end.
Assuming we take this to be the only rule governing stalemates, is it possible for the game to go on for eternity or will it always end, no matter how long it takes?
That’s a simple answer. Since even chess has a limited number of moves (even if there are very, very many), the only thing that will allow it to go on forever is repetition. So it will always end. Eventually.
(But yes, there is also the 50 move without a strike rule that will end a game in a stalemate, iirc)
Stalemate is one way to end a game (as a draw). It occurs only when the player to move has no legal moves with any of their pieces, but is not in check.
If the same position, with the same player to move, and with all the same legal moves (i.e. if a player could castle the first time the position occurred, they must be able to in the following positions), occurs 3 times, then the player to move can claim a draw. This is called draw by repetition (not stalemate).
They don’t have to claim.
I remember a last round British Championship game between Grandmaster Hodgson + another leading player where both players needed to win for a chance at the title. The same position arose 6 times (!), before both players decided it was too risky not to take the draw.
Chess has a limited number of positions. This is approximately 2 * 10^43.
The number of different 40 move games has been estimated as 25 * 10 ^115.
The 50 move rule occurs when neither player has moved a pawn or made a capture for 50 moves. This is indeed a draw but is not stalemate!
The longest possible legal game is estimated to finish on move 5,949.
In 1980, a genuine game took 193 moves.
All statistics are from the excellent ‘The Complete Chess Addict’ by Fox and James.
Few clarifying questions:
glee: I’m assuming the game can only end when
I think the maximum move number woud be far more than 5000 given these rules, consider the case of 2 kings and one black rook, the rook is at a1 and the black king is at a2. Every black move, the king moves from a2 to b1 and then back to a2. This effectively means that the white king can move anywhere in a 7x7 area minus 3 squares from the top so 46 squares. I don’t know how exactly to work out the number of unique traversals of 46 squares but I assume it would include combinatorics in there somewhere.
Well OK, but that’s not a chess game.