Saturday, December 04, 2021

[honhnynk] endgames on infinite boards

investigate chess endgames on infinite boards (including half infinite, quarter infinite, 1/8 infinite) by investigating them on sufficiently large but finite boards.  if the defending king makes it to certain edges, it is deemed to have a strategy that escapes to infinity so the game is drawn.

because everything is finite, tablebases are possible.

these finite regions only approximate infinity, but perhaps a sufficiently large regions can approximate infinity close enough for the endgame evaluation to be exact.

this probably has a chance of working only if the defending side does not have ranged pieces (bishop, rook, queen).

many tricky details remain.  might not work at all.

vaguely similar to angel versus square eater.

this will not work on a chess variant in which perpetual check wins.

previously, endgames on arbitrary but finite boards.

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