[Retros] Illegal moves by grandmasters

tregeryefim at aol.com tregeryefim at aol.com
Tue May 10 14:09:29 EDT 2011

The (composed) dead positions published by Andrew Buchanan are indeed illegal as no legal game can be construed to arrive at them. The "law" does not always look the same in forward and backward direction.
What does "legal game" mean? This term is also may have several meanings. Upon Fide rules, indeed, a game cannot contain two or more dead positions. But we may consider a game as a sequence of any legal positions, regardless of fide rules (of dead positions, 3-times, 50 moves, etc.). Then there is a set of all such legal games (even infinite ones!) as a mathematical object... Interesting that this set is uncountable (why - I may explain it separately), yet the subset of all finite games (finishing by checkmate or stalemate positions) is countable.

Yefim Treger
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