Body: <p>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.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T13:58:10.600Z
Comments.Text: Related: https://chess.stackexchange.com/a/37283/33999
Comments.UserDisplayName: Matija Sirk
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T14:06:16.143Z
Comments.Text: I think there should be a formula that depends on N.
Comments.UserDisplayName: nirates biadenroc
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T14:55:24.343Z
Comments.Text: 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...
Comments.UserDisplayName: Evargalo
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T15:04:33.923Z
Comments.Text: I think we need to formulate it. And why?
Comments.UserDisplayName: nirates biadenroc
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T16:13:39.760Z
Comments.Text: Related, but ignoring 50 move rule, longest DTM in 7-piece tables is 549 (https://tb7.chessok.com/articles/Top8DTM_eng).
Comments.UserDisplayName: Matija Sirk
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T16:58:24.580Z
Comments.Text: Actually, you can ignore the 50 move rule because it is not a mandatory draw, but you can't ignore the mandatory ones.
Comments.UserDisplayName: nirates biadenroc
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T19:39:14.360Z
Comments.Text: Why do you think there would be a formula?  I'd be amazed if there was one.
Comments.UserDisplayName: Peter Flom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T20:02:53.940Z
Comments.Text: Perhaps there really is, who knows?
Comments.UserDisplayName: nirates biadenroc
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T20:18:33.900Z
Comments.Text: 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.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-12T21:13:32.340Z
Comments.Text: Perhaps it might be useful in building strategy, I guess.
Comments.UserDisplayName: nirates biadenroc
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-13T02:13:36.007Z
Comments.Text: You don't have to worry about dead position rule here; if the position was dead then checkmate would be impossible anyway.
Comments.UserDisplayName: D M
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-02-13T10:01:02.783Z
Comments.Text: If the position is about to reach there, I think we should.
Comments.UserDisplayName: nirates biadenroc
Tags: <analysis><theory>
Title: DTM in a random N-piece position
ThreadText: # DTM in a random N-piece position
  
  (Asked by: username_0 on 2024-02-12)
  
  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.
  
  **Tags:** analysis, theory
  
  > **Comments:**
  > **username_1**: Related: https://chess.stackexchange.com/a/37283/33999  
  > **username_0**: I think there should be a formula that depends on N.  
  > **username_2**: 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...  
  > **username_0**: I think we need to formulate it. And why?  
  > **username_1**: Related, but ignoring 50 move rule, longest DTM in 7-piece tables is 549 (https://tb7.chessok.com/articles/Top8DTM_eng).  
  > **username_0**: Actually, you can ignore the 50 move rule because it is not a mandatory draw, but you can't ignore the mandatory ones.  
  > **username_3**: Why do you think there would be a formula?  I'd be amazed if there was one.  
  > **username_0**: Perhaps there really is, who knows?  
  > **username_4**: 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.  
  > **username_0**: Perhaps it might be useful in building strategy, I guess.  
  > **username_5**: You don't have to worry about dead position rule here; if the position was dead then checkmate would be impossible anyway.  
  > **username_0**: If the position is about to reach there, I think we should.  
  
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  ## 0 answers
  
  