Monday, February 27, 2012

[blxawpwq] Stalemate vs Checkmate

To simplify the rules of chess, suppose the game is played until king capture.  This increases the number of legal moves, though all of these newly legal moves lose immediately by the opponent's response.

Stalemates become tricky to define.  However, thinking this way allows us to distinguish between two types of stalemates: In the first type, the only moves available place the king in check (but the king is not currently in check; that would be checkmate).  In the second type, there are actually no moves available (not even these newly legal ones which place the king in check).  One might propose new rules where the two cases are treated differently.

To distinguish between checkmate and stalemate (first type), one needs to do a counterfactual null move analysis.  Is the king currently in check?  That is, if passing were a legal move (it's not), and if the player were to pass, then could the opponent capture the king the next move?  It's kind of weird that scoring the game relies on considering an illegal type of move (passing).

I propose eliminating this nit by saying stalemate (first type) and checkmate are the same.  Stalemate (first type) merely becomes an extreme form of zugswang.

Stalemate (second type) is a draw, but I predict it will occur extremely rarely.  Alternatively, it's the only time a player is permitted to pass.  Even so, mutual second-type stalemate would have to be a draw.  (Construct such a position and a proof game.)

The prohibition of castling through check could be translated to a variation of an en passant rule: the king can be captured by attacking any of the squares it passed through, including the starting square.  (But not the rook.  It is philosophically assumed to have moved first, which is different from how the move is required to be physically executed.)

Another play-til-king-capture proposal

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