2

Normally I'd pester the/a computer chess forum, but I couldn't register yet...

On the Matplus chess forum, the following construction task came up.

Both White and Black are on the brink of losing because the position is so sharp. Both players have only one way to draw the game. However, the seqeunce falls under th Nunn convention-each move is the only one that doesn't lose, but it has at least one legal alternative. They are denoted as “!” moves. What is the longest sequence of mutual "!" moves?

Here is an illustrating example:

[FEN "2K5/8/7k/6N1/3q1N2/8/8/8 w - - 0 1"]

1. Nf7+ Kh7 2. Ng5+ Kh6 3. Nf7+

Nalimov confirms that 1.Sf7+! Kh7 2.Sg5+! Kh6! is the only way to draw (by repetition), but since Kh7 is also an only legal move, this position is invalid.

I don't have Nunns "Secrets" series at hand, where surely some examples can be found. Neither can Imine a database for this question. Maybe you can?

  • ! = the only move that doesn't change the result of the game, among at least an alternative. (The promotion stuff is only relevant for a record - I'm just doing a background research.) – Hauke Reddmann Apr 9 '19 at 17:31
  • OK - any chess position has an objective result under best play of both sides (even if we might be too stupid to know :-), which is win, draw or loss for White. Obviously, only in a drawn position both players can blunder, i.e. make a theoretically drawn position a loss for them by their move. – Hauke Reddmann Apr 9 '19 at 17:38
  • I don't believe that your definition of ! can be evaluated in polynomial time. – Acccumulation Jun 13 '19 at 19:55
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The example below comes from Guy Haworth's Chess Endgame Records.

The annotations, as explained by Guy Haworth, are as follows:

% the only move available
! the only value-preserving move available (i.e., for a White move, the only winning move, and, for a Black move, the only drawing move, all others losing)
''' the only move which does not allow a repetition or otherwise waste time
'' the unique optimal move selected by the defined strategy
' an optimal but not unique optimal move

The other notation used is as follows (this is copied from Guy Haworth's book):

Metrics: DTM Depth To Mate

Miscellaneous notation:
AUMS Absolutely Unique Move Sequence

[White "KR"]
[Black "KNP"]
[Result "1-0"]
[Date "2013.11.24"]
[Event "5m, 2-3m, KRKNP, GBR 0103.01, longest-known decisive AUMS: SV+M+/SUm"]
[Annotator "Haworth, Guy"]
[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} *

Each of the first 35 plies, from White's 1st to White's 18th move, is the unique best for the player. What move is best for Black on their 18th turn depends on the criterion applied. Black's 18th move here, 18 ... Ne1, is the unique move which enables Black to maximise the number of successive White turns at which White has only one winning option. However, if Black is to maximise the number of future turns (i.e. maximise DTM), Ne1 is not best for Black: it loses for Black in 20; best is 18 ... Ne3+ (loses in 32) 19 Kc6 (best; wins in 32; Kc5 wins in 34).

  • Interesting too, but not the answer to the original question! Black is always lost, his moves are "best" only in the sense that he can hold out longest with exactly 1 move each time. – Hauke Reddmann Apr 13 '19 at 14:37
  • This is a really useful notation which I will apply in the future. Thanks for posting! – Laska Dec 17 '19 at 6:12
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Just to add a note of interest for the people of CSE (excluding Hauke of course who knows of this), here's the current known of record of 32 ply by Geir Sune Tallaksen Østmoe, borrowed from the question's linked Matplus foums.

The question is asking for the longest, or an example of, series of both sides that are the only drawing move that is dual free in a position without promoted pieces. This is under the Nunn Convention, which, to my understanding, means that there must be at least one other legal moves and pawn promotions count as duals.

I do not know of any studies myself, but perhaps I will find something someday. I if I do, I shall update this answer.

Now, here is that 32-ply record.

[Title "Geir Sune Tallaksen Østmoe, Apr 9, 2019 "]
[FEN "k1B5/r1p1p2b/nPPP2R1/BN2b1R1/2P2qp1/p7/P3P2P/6nK w - - 0 1"]

1. Bb7+ Rxb7 2. Rg8+ Bxg8 3. Rxg8+ Nb8 4. Rxb8+ Kxb8 5. bxc7+ Rxc7 6. dxc7+ Bxc7  7. Bxc7+ Qxc7 8. Nxc7 Kxc7 9. Kxg1 Kxc6 10. Kf2 Kc5 11. Kg3 Kxc4 12. Kxg4 Kc3  13. h4 Kb2 14. h5 Kxa2 15. h6 Kb1 16. h7 a2
  • White is winning here, right? – justhalf Jun 7 '19 at 19:14
  • How is 10.Kg2 losing ? – Evargalo Jun 11 '19 at 11:27

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