# DTM in a random N-piece position

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.

• Feb 12 at 13:58
• I think there should be a formula that depends on N. Feb 12 at 14:06
• Related, but ignoring 50 move rule, longest DTM in 7-piece tables is 549 (tb7.chessok.com/articles/Top8DTM_eng). Feb 12 at 16:13
• Why do you think there would be a formula? I'd be amazed if there was one. Feb 12 at 19:39
• Of 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. Feb 12 at 20:18