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I know that is winning for White because of the Syzygy tablebases. But Stockfish 14.1 NNUE, without tablebases, returns an evaluation of only +3.23 at depth =72(!). What is White's DTM?

[FEN "8/5N2/6p1/R5Pk/8/4K3/8/6r1 b - - 0 1"]
[startflipped ""]
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  • Knight on f7. I missed the keyboard
    – Stefano
    Feb 11 at 17:48
  • Lomonosov does not work in my country right now.
    – Stefano
    Feb 11 at 17:52
  • 6
    I see you've consistently posted questions without using the replayer to show the position as a diagram. I strongly encourage you to consider using it. See How do I add a replayer to my post?. I think you'll get a more positive response to your questions. Feb 11 at 17:52

2 Answers 2

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The tablebase in the Lichess analysis tool gives 35 moves.

[FEN "8/5N2/6p1/R5Pk/8/4K3/8/6r1 b - - 0 1"]
[startflipped ""]
      
1... Rf1 2. Nd8 Kg4 3. Rd5 Ra1 4. Nf7 Rf1 5. Rd4+ Kh5 6. Rf4 Re1+ 7. Kf3 Re3+ 8. Kf2 Re2+ 9. Kg3 Rg2+ 10. Kf3 Ra2 11. Rf6 Ra4 12. Ke3 Ra1 13. Kf4 Ra5 14. Kg3 Ra3+ 15. Rf3 Ra4 16. Rf1 Ra1 17. Rf2 Ra3+ 18. Kf4 Ra4+ 19. Ke5 Ra6 20. Rd2 Rb6 21. Rd6 Rb4 22. Kf6 Rd4 23. Rd8 Rf4+ 24. Kg7 Rf1 25. Rd6 Ra1 26. Rxg6 Rb1 27. Ra6 Ra1 28. Rxa1 Kg4 29. Rf1 Kg3 30. g6 Kg2 31. Rf6 Kg1 32. Kh7 Kh1 33. g7 Kg1 34. g8=Q+ Kh1 35. Rh6#
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  • Please teach me how to include the diagram properly. It looks correctly in the edit preview and then it shows the default starting position in the answer. Feb 12 at 21:56
  • That looks like a bug. There have been problems with this recently that were supposed to be fixed but clearly still aren't. Any ideas @Glorfindel ?
    – Brian Towers
    Feb 13 at 0:23
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I can't give an exact DTM answer, but this one will be off by only a few moves. If you replay the Syzygy line, you will see Black can only annoy White with countless stalemate shenanigans, but White will finally get Pg6 at move 48 (phew), closely making it within the 50 move rule. Since anything DTM strategy which may be globally faster surely is in danger fail due to the 50 move rule, we can safely assume the play is optimal for White, leading to e.g. this position (BTM):

[FEN "8/5NK1/6R1/6Pk/8/8/8/r7 b - - 0 1"]
[startflipped ""]

This can already put into a DTM tablebase. I only have Shredder Nalimov; Black must very fast sacrifice the rook, so 16 moves seem to be DTM. So I think I can safely say DTM #65+-5.

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