what is the longest tablebase mate with special properties?

[Uri Blass]

I define that a mate is with a single path for the winner if the winner has only one move for the shortest mate regardless of the opponent choice.
I define that a win is with a single path for the winner if the winner has only one move to win the game.
I define complexity of mate as the number of possible lines that can happen until the mate assuming both sides play perfectly.

The question is what is the longest mate with special properties(it is possible to run some program on tablebases to find
the reply for tablebases positions).

1)what is the longest mate with a single path to mate
2)what is the longest mate with a single path to win the game
3)what is the biggest complexity that mates with a single path to the shortest mate have
4)What is the biggest complexity that mates with a single path to win the game have

Examples:


[d]k7/3Q4/8/8/8/8/8/7K w - - 0 1

Thia position is a mate in 6 with a single path because white has only one winning move that is the shortest way to mate regardless of the choice of black.

I can define the complexity of this mate 1 because the defender has no choice so there is only a single line to show to prove it is a mate.

[d]2k5/8/2K5/2R5/2p5/8/8/8 w - - 0 1

This position is a mate in 3 with a single path for white for the shortest mate.
complexity of it is 2 because there are 2 ways for black to respond in the first move.

[d]k7/P7/8/1K4p1/8/8/1P6/8 w - - 0 1

This position is a mate in 5 with a single path for white to win the game(there is no way not to play the shortest mate without missing the win).
complexity of it is 4 because there are 4 ways for black to promote a pawn in the last move.

[jp]

The question is what is the longest mate with special properties (it is possible to run some program on tablebases to find the reply for tablebases positions).

Do you mean you have written a program that does this kind of thing? Such a program would be very useful.

[Uri Blass]

No

I did not write a program to do it.

My point was that it is possible to do it.

[jp]

Examples:

[d]2k5/8/2K5/2R5/2p5/8/8/8 w - - 0 1

This position is a mate in 3 with a single path for white for the shortest mate.
complexity of it is 2 because there are 2 ways for black to respond in the first move.

This is not actually a single path for White. If Black responds to 1.Rxc4 with 1... Kb8, White has two ways to respond (Ra4, Kb6) with equal DTM.

This is fixable, though: just shift all the pieces to the d- or e-file.

[jp]

[d]r6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1

This is mate in 9, with a single path:

1.Rxa8+ Kxa8 2. Kc7 Ka7 3. h3! Ka8 4. h4 Ka7 5. h5 Ka8 6. h6 Ka7 7. h7 Ka8 8. h8=Q+ Ka7 9. Qb8#

(1... Kb7 allows mate in 6, so the complexity is only 1.)

Strictly, though, the tablebases don't show at the start that 1.Rxa8+ is the shortest mate, because for 7 pieces we have only DTZ. DTMs are shown only after the exchange.

[Andrew]

Examples:

[d]2k5/8/2K5/2R5/2p5/8/8/8 w - - 0 1

This position is a mate in 3 with a single path for white for the shortest mate.
complexity of it is 2 because there are 2 ways for black to respond in the first move.

This is not actually a single path for White. If Black responds to 1.Rxc4 with 1... Kb8, White has two ways to respond (Ra4, Kb6) with equal DTM.

This is fixable, though: just shift all the pieces to the d- or e-file.

Uri, did you mean a single move for the first move only, or a single move for all of whites moves?
Both are interesting questions!

Andrew

[Andrew]

This is mate in 9, with a single path:

1.Rxa8+ Kxa8 2. Kc7 Ka7 3. h3! Ka8 4. h4 Ka7 5. h5 Ka8 6. h6 Ka7 7. h7 Ka8 8. h8=Q+ Ka7 9. Qb8#

(1... Kb7 allows mate in 6, so the complexity is only 1.)

Strictly, though, the tablebases don't show at the start that 1.Rxa8+ is the shortest mate, because for 7 pieces we have only DTZ. DTMs are shown only after the exchange.

1 Rh7+ ? (mate in 3)

Andrew

[abulmo2]

[d]r6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1

This is mate in 9, with a single path:

1.Rxa8+ Kxa8 2. Kc7 Ka7 3. h3! Ka8 4. h4 Ka7 5. h5 Ka8 6. h6 Ka7 7. h7 Ka8 8. h8=Q+ Ka7 9. Qb8#

(1... Kb7 allows mate in 6, so the complexity is only 1.)

Strictly, though, the tablebases don't show at the start that 1.Rxa8+ is the shortest mate, because for 7 pieces we have only DTZ. DTMs are shown only after the exchange.

Is not this a mate in 3?
[pgn]
[Event "Edited position"]
[Site "rpi4"]
[Date "2020.12.14"]
[Round "-"]
[White "-"]
[Black "-"]
[Result "1-0"]
[FEN "r6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1"]
[SetUp "1"]

1. Rh7+ Kb8 2. Kc6 Ra7 3. Rh8# {Checkmate} 1-0
[/pgn]

[Uri Blass]

[d]r6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1

This is mate in 9, with a single path:

1.Rxa8+ Kxa8 2. Kc7 Ka7 3. h3! Ka8 4. h4 Ka7 5. h5 Ka8 6. h6 Ka7 7. h7 Ka8 8. h8=Q+ Ka7 9. Qb8#

(1... Kb7 allows mate in 6, so the complexity is only 1.)

Strictly, though, the tablebases don't show at the start that 1.Rxa8+ is the shortest mate, because for 7 pieces we have only DTZ. DTMs are shown only after the exchange.

Is not this a mate in 3?
[pgn]
[Event "Edited position"]
[Site "rpi4"]
[Date "2020.12.14"]
[Round "-"]
[White "-"]
[Black "-"]
[Result "1-0"]
[FEN "r6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1"]
[SetUp "1"]

1. Rh7+ Kb8 2. Kc6 Ra7 3. Rh8# {Checkmate} 1-0
[/pgn]

You are right.
trying to fix it to single path but it is not good enough because after 1.Rxa8+ kb7 it is a shorter mate
so it is not a single path based on my definition.
[d]rR6/k7/p2K4/P7/8/8/7P/8 w - - 0 1

[Uri Blass]

A better fix

[d]q7/k7/p2K4/P7/8/8/7P/7Q w - - 0 1

single path to mate in 9.

No single path to win the game because 1.Qg1+ also win the game