On Fri, Nov 13, 2020 at 2:10 PM James Propp <jamespropp@gmail.com> wrote:
Ordinary chess forbids moving into check (and hence from moving into checkmate), which means you automatically lose if there's no way to avoid moving into check.
Those aren't the rules of chess. If you have no legal move (and a move which would put your own king in check is illegal), then you do not lose; the game is a draw. This is called "stalemate". This rule leads to different outcomes in some important endgames, especially K + P vs. P, where some games that would be winnable if a player with no legal moves lost, and would also be winnable if moving into check was legal and the game ended when the king was captured, are actually draws. Assuming all players are good enough to detect positions where the king could be captured, if no legal moves was a loss, then the outcome of any game under "capture the king wins", and "exposing your king to capture" would always be exactly the same. You'd just be stopping games one move earlier whenever the outcome is inevitable. You can perform this operation on any game where not being able to move is a loss, making all moves which lead to an immediate loss illegal. Conway has some name for this operation in Winning Ways, because while it doesn't effect the outcome of a game, it may affect the outcome of certain kinds of sums of games where this game is a component. Similarly, if we take chess with the modification that no legal moves is a loss rather than a draw, then prohibiting any move which leads to a forced capture of the king in two moves has no effect on the game as long as all players are good enough to see all mate-in-1 positions (and if they are not, they cannot determine the legality of moves in this version of the game); this is just performing this operation, which doesn't change the outcome of a game, twice, which still leaves the outcome unchanged. If we take the actual chess rules, where having no legal moves is a stalemate draw, then I think that prohibiting a move that leads to a forced capture of the king in two moves (or equivalently, allows a mate in 1) leads to a game that is an easy draw for minimally competent players. Here's the simple drawing strategy. If all moves lead to mate in 1, the game is a stalemate draw, by the new rule. If there is at least one move that does *not* lead to a mate in 1, make any such move. This strategy cannot be defeated, so the game is a draw unless someone blunders by allowing a mate in 1 where a different move would avoid it. Andy
Is there a variant of chess in which you're not allowed to make a move that would cause you to lose 2 moves in the future?
(Replacing 2 by larger integers, we get a game in which the legality of a move can become rather murky!)
Jim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com