Thursday, August 04, 2022

[rpnzkdxr] chess960 simultaneous round robin

a round robin chess tournament with 44 participants has 946 games.  this is the largest possible staying under the 960 possible initial positions of chess960.  (of course, you don't have to go all the way to the maximum possible number of participants.)

idea is to play all games simultaneously but prevent the sleazy trick of when a participant X plays simultaneous games against Y and Z, X induces Y to play against Z by channeling moves between them.  if all games start from different initial positions, then this is less likely.  it's still possible through transposition.  can a player make it more likely to happen?

initial positions differing only by mirror symmetry (castling) seem the most likely to "channel".  first, randomly discard one of each mirror image pair, then draw (without replacement) initial positions from the remaining 480 possibilities.  max 31 players, 465 games.

Basque system possible.

future work: using careful assignment, it seems possible to have more players, still preventing channeling.

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