Longest series of mutual “!” moves

Question

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?

Answer 1

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).

Answer 2

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