[math-fun] Chess underpromotions etc
The P=B game examples are new to me and v welcome: I had thought there were none over the board that were 'essential'. P=N is not strictly an underpromotion but an 'underpromotion' - as the Knight can do things the Queen cannot do. The maxDTM[ate] KRPPKRP btm loss requires White to genuinely underpromote to a Rook in a 'Saavedra'-like position ... in order to win in 217 moves, q.v., http://centaur.reading.ac.uk/34268/ The maxDTM KRNPKPP loss, also at http://centaur.reading.ac.uk/34268/ , has Black making two P=N promotions to maximise the depth of mate: dtm = 182m. FIDE briefly varied the 50-move rule with a 100-move rule in various circumstances - but realised, with the 6-man results (maxDTC[onversion] = 243m) that this was not a finite game. Now all is back to a 50-move rule ... except there is a 75-move rule (that the game will end as a draw without need of a claim) coming in at the end of June 2014. Tournament arbiters can waive a rule if they wish, provided they are happy for the games not to be FIDE rated ... which doesn't apply to Computer-Computer games. The Lomonosov 'MVL' team in Moscow completed 7m DTM EGTs in 2012 for all except 6-1m endgames and positions with non-null casting rights. Interestingly, the new World Champion, Carlsen, said (only a few weeks ago) that 7m EGTs would never be done in his lifetime. Guy
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Guy Haworth