Formulate how many plies are the DTMs if there are multiple checkmate variations (Depth to Mate ignoring 50-move rule) for a random N-piece chess position if any checkmate exists, (and also consider the positions that there is only one checkmate variation) (N is at most 32). Consider the condition that one checkmates the other, not draw. (without neglecting ONLY THE MANDATORY FIDE draw rules and the DEAD POSITION rule). Assume that losing side tries to maximize DTM and winning side tries to minimize DTM (Losing side fighting to delay checkmate, winning side trying to deliver the checkmate as quickly as possible) such that both sides play optimally starting from the position.
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Related: https://chess.stackexchange.com/a/37283/33999 – Matija Sirk Feb 12 '24 at 13:58
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I think there should be a formula that depends on N. – nirates biadenroc Feb 12 '24 at 14:06
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For N=3, it will be the longest KRK mate (around 35 plies). For N=4, it's interesting to investigate (KQKR, KRKN, KBNK or even some KPKP ?). For N>4 I'm afraid you will never have the answer... – Evargalo Feb 12 '24 at 14:55
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I think we need to formulate it. And why? – nirates biadenroc Feb 12 '24 at 15:04
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1Related, but ignoring 50 move rule, longest DTM in 7-piece tables is 549 (https://tb7.chessok.com/articles/Top8DTM_eng). – Matija Sirk Feb 12 '24 at 16:13
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Actually, you can ignore the 50 move rule because it is not a mandatory draw, but you can't ignore the mandatory ones. – nirates biadenroc Feb 12 '24 at 16:58
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3Why do you think there would be a formula? I'd be amazed if there was one. – Peter Flom Feb 12 '24 at 19:39
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Perhaps there really is, who knows? – nirates biadenroc Feb 12 '24 at 20:02
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4Of course there's a formula because there are only finitely many data points (even if we'll never compute them all) and one can always do a polynomial fit. But it's not a useful formula. – Noam D. Elkies Feb 12 '24 at 20:18
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Perhaps it might be useful in building strategy, I guess. – nirates biadenroc Feb 12 '24 at 21:13
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You don't have to worry about dead position rule here; if the position was dead then checkmate would be impossible anyway. – D M Feb 13 '24 at 02:13
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If the position is about to reach there, I think we should. – nirates biadenroc Feb 13 '24 at 10:01