what is the longest tablebase mate with special properties?

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Uri Blass
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what is the longest tablebase mate with special properties?

Post by Uri Blass » Sun Dec 13, 2020 4:40 am

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:




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.



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 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
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Re: what is the longest tablebase mate with special properties?

Post by jp » Sun Dec 13, 2020 6:22 am

Uri Blass wrote:
Sun Dec 13, 2020 4:40 am
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
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Re: what is the longest tablebase mate with special properties?

Post by Uri Blass » Sun Dec 13, 2020 6:26 am

No

I did not write a program to do it.

My point was that it is possible to do it.

jp
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Re: what is the longest tablebase mate with special properties?

Post by jp » Mon Dec 14, 2020 4:16 am

Uri Blass wrote:
Sun Dec 13, 2020 4:40 am
Examples:



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.
Last edited by jp on Mon Dec 14, 2020 4:32 am, edited 2 times in total.

jp
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Re: what is the longest tablebase mate with special properties?

Post by jp » Mon Dec 14, 2020 4:30 am



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
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Re: what is the longest tablebase mate with special properties?

Post by Andrew » Mon Dec 14, 2020 6:30 am

jp wrote:
Mon Dec 14, 2020 4:16 am
Uri Blass wrote:
Sun Dec 13, 2020 4:40 am
Examples:



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
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Re: what is the longest tablebase mate with special properties?

Post by Andrew » Mon Dec 14, 2020 6:47 am

jp wrote:
Mon Dec 14, 2020 4:30 am

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
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Re: what is the longest tablebase mate with special properties?

Post by abulmo2 » Mon Dec 14, 2020 7:54 am

jp wrote:
Mon Dec 14, 2020 4:30 am


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?
Richard Delorme

Uri Blass
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Re: what is the longest tablebase mate with special properties?

Post by Uri Blass » Mon Dec 14, 2020 8:11 am

abulmo2 wrote:
Mon Dec 14, 2020 7:54 am
jp wrote:
Mon Dec 14, 2020 4:30 am


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?
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.

Uri Blass
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Joined: Wed Mar 08, 2006 11:37 pm
Location: Tel-Aviv Israel

Re: what is the longest tablebase mate with special properties?

Post by Uri Blass » Mon Dec 14, 2020 8:16 am

A better fix



single path to mate in 9.

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

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