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Having been inspired by an article on ChessBase.com, what is the longest current tablebase mate with a unique optimal line?

By unique, I mean for each of the winning side's plies, there is only one move that gives a shortest forced mate. and for each of the losing side's plies, there is only one move that gives a longest forced mate.

  • What does unique optimal line mean? Do you mean, there is only one option in each move? – ferit Jan 20 '16 at 21:45
  • I mean {for each of the winning side's plies, there is only one move that gives a shortest forced mate} and {for each of the losing side's plies, there is only one move that gives a longest forced mate}. ​ ​ – user2668 Jan 20 '16 at 23:44
  • Got it. I bet its not longer than 30 moves. – ferit Jan 20 '16 at 23:48
  • I remember I saw something like forced-mate in 250 moves. – SmallChess Jan 21 '16 at 1:43
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    Those maximal-length wins are almost never unique even in the weaker sense (that's more standard in chess problems) that at each point the defender has at least one (co-)optimal move that makes the attacker's reply unique. If I remember right, the ending KBN/K has such a line that's a mate in 30 or so. – Noam D. Elkies Jan 21 '16 at 1:51
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Guy Haworth gives an answer to this in his Chess Endgame Records.

[fen "8/8/7p/7n/k7/8/2K5/3R4 w - - 0 1"]

1. Rd4+! {dtc/m/z = -26/-49/-17m} Ka3 2. Kd3! Kb3 3. Rd6! Kb4 4. Kd4! Nf4 5. Rb6+! Ka5 6. Rf6! Ne2+ 7. Kc4! Ng3 8. Rg6! Ne4 9. Kd4! Nd2 10. Rg2! Nf3+ 11. Kc5! Ka6 12. Rg6+! Kb7 13. Kd5! h5 14. Rh6! h4 15. Rf6! Ne1 16. Rf1! Nc2 17. Rb1+! Ka6 18. Rb2! Ne1 19. Ke4! h3 20. Rb1! Nc2 21. Kd3! Na3 22. Ra1! h2 23. Rxa3+! {KRKP: dtc/m/z = -3/-15/-3m} {Nalimov and Lomonosov DTM EGTs} *

Haworth states that this is the longest-known decisive AUMS, Absolutely Unique Move Sequence, known to the author.

This move-sequence arose from White and Black adopting the following strategies. White's strategy is: first, preserve the value, i.e. keep the position won for White; second, maximize DTM. (Why "maximize" and not "minimize"? I don't know, but in the above line White has only one value-preserving option at each move anyway, so it doesn't matter.) Black's strategy is to challenge White to find the unique value-preserving move.

Every move in the above line is optimal for the player's strategy. In the cases of Black's 20th and 22nd moves, there is not one unique option which is optimal for Black's strategy, but for all Black's other moves the move given above is Black's only option which implements Black's strategy of giving White only one option which keeps the position won for White.

Note that the identity and length of the longest decisive AUMS depends on what White's and Black's strategies are. Black's strategy of preferring "restrict White to a unique winning move" seems calculated to enable there to be long AUMSes. If, instead, Black adopts the strategy "maximize DTM", then the game proceeds differently. 18...Ne1 is indeed Black's only option which gives White only one winning move, but it loses in 20 moves. By contrast, 18...Ne3 loses in 32 (i.e. keeps Black alive for 12 moves more); 19. Kc6 then wins in 32, and 19. Kc5 in 34.

Some of the jargon explained:

decisive: ending in checkmate, not in stalemate

AUMS: Absolutely Unique Move Sequence

DTC: depth to conversion (i.e. depth to capture, promotion, or the end of the game)

DTM: depth to mate

DTZ: depth to changing which ply is the earliest at which a 50-move-rule draw may be claimed (i.e. depth to capture, pawn-move, or the end of the game)

value: whether the position is (with best play) won for White, won for Black, or drawn

Upper-case DTC/M/Z refer to white; lower-case dtc/m/z refer to Black.

Depth is measured in plies, where a ply is either a white move or a black move.

Haworth cites Conrady, 2003; van der Heijden #70232, (2010). The relevant entries in his bibliography are:

Conrady H. (2003). Computerschach und Spiele, Vol. 2, No. iv-v

van der Heijden, H. (2010). http://www.hhdbiv.nl/. ENDGAME STUDY DATABASE IV

The longest AUMS I can see in Haworth which ends with the mating move is a 13-ply KNkp mate. Using Nalimov I have extended it back for a further two plies but only by dint of captures.

[fen "8/8/8/1p6/b1R5/8/N7/k1K5 w - - 0 1"]

1.Rxa4! bxa4 2.Nb4! a3 3. Nc2+! Ka2 4. Nd4! Ka1 5. Kc2 Ka2 6. Ne2 Ka1 7. Nc1 a2 8. Nb3#! {Nalimov and Lomonosov DTM EGTs} *
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    Strictly speaking this uses a different definition of optimal than the (comment below the) question. – RemcoGerlich May 27 '16 at 10:35
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    Thanks for alerting me to that. I have added a move-sequence which is optimal on that basis all the way to checkmate. It is only a stopgap and I make no claim that it is the longest. – Rosie F May 27 '16 at 12:10
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As far as I understand it, tablebase positions are any positions with 7 pieces or less since that ismthe current limit. Chess composers have a knack for creating problems with unique solutions, as well as problems with 7 pieces or less, which are known as miniatures.

I looked for long “miniatures” in chess problem databases that had a unique solution for both White and Black, i.e. there are no alternative moves at any point nor are their any promotion duals.

As far as I have searched, here is the longest unique tablebase mate in 39 ply long, and it was found at the Schwalbe PBD.

[Title "Victor Cuciuc, E191 diagrammes, 8/5/1984, Mate In 20 Moves"]
[FEN "8/P7/8/8/8/n6q/2p2K2/r6k w - - 0 1"]

 1. a8=Q+ Kh2 2. Qb8+ Kh1 3. Qb7+ Kh2 4. Qc7+ Kh1 5. Qc6+ Kh2 6. Qd6+ Kh1 7. Qd5+ Kh2 8. Qe5+ Kh1 9. Qxa1+ Nb1 10. Qa8+ Kh2 11. Qb8+ Kh1 12. Qb7+ Kh2 13. Qc7+ Kh1 14. Qc6+ Kh2 15. Qd6+ Kh1 16. Qd5+ Kh2 17. Qe5+ Kh1 18. Qe1+ Qf1+ 19. Qxf1+ Kh2 20. Qg2#

While there are longer miniatures with queen “staircases,” as this problem uses, they do not have unique lines all the way through.

With just 6 pieces, 31 ply is the longest sequence that I know of.

[Title "Johannes Steinmüller, Schach 12/1996"]
[FEN "8/3p4/8/8/8/p1p5/2K5/k4N2 w - - 0 1"]

1. Ng3 Ka2 2. Ne2 Ka1 3. Nc1 d5 4. Ne2 Ka2 5. Nxc3+ Ka1 6. Ne2 Ka2 7. Nd4 Ka1 8. Nc6 Ka2 9. Nb4+ Ka1 10. Kc1 d4 11. Nc2+ Ka2 12. Nxd4 Ka1 13. Kc2 Ka2 14. Ne2 Ka1 15. Nc1 a2 16. Nb3#
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