I meant for all moves for the winner when the moves of the loser change nothing and the comment that it is not actually a single path but easy to fix is correct.Andrew wrote: ↑Mon Dec 14, 2020 7:30 amUri, 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
what is the longest tablebase mate with special properties?
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Re: what is the longest tablebase mate with special properties?
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Re: what is the longest tablebase mate with special properties?
[d]k7/P3p3/1q2Pp2/K1p1pP2/1pPpPp2/1P1P1P2/B7/b7 w - - 2 1
This is probably mate in 11 with a single path for the winner.
The loser has a lot of option and did not calculate complexity for it.
It is not a single path to win except the first move.
This is probably mate in 11 with a single path for the winner.
The loser has a lot of option and did not calculate complexity for it.
It is not a single path to win except the first move.
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Re: what is the longest tablebase mate with special properties?
Oh, Andrew & RIchard are right. I got fooled by the (DTZ) tablebase.Andrew wrote: ↑Mon Dec 14, 2020 7:47 am1 Rh7+ ? (mate in 3)jp wrote: ↑Mon Dec 14, 2020 5:30 am [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.
Here's the safe but somewhat ugly fix:
[d]q6R/k7/p2K4/P7/8/8/7P/8 w - - 0 1
Mate in 9 with a single path, as previously claimed.
[Note: I see Uri's fix on the bottom of the previous page too.]
Last edited by jp on Tue Dec 15, 2020 7:34 am, edited 1 time in total.
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Re: what is the longest tablebase mate with special properties?
It's true that 1... Kb7? allows the shorter mate e.g. 2. Rh8 (or Rg8, etc.) Ka7 3. Rh7+ Kb8 4. Kc6 Ka8 5. Kb6 Kb8 6. Rh8#...
But surely it is single path (or the definition should allow it to be)?
Because 1... Kb7 is not Black's best move. I'd want the definition to mean that the defender puts up the stiffest opposition.
I was assuming the same (best defensive moves) for the complexity definition too, i.e. that there are multiple paths only if the defender's multiple moves all have the same DTM. Maybe we need extra definitions.
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Re: what is the longest tablebase mate with special properties?
Extra terminology:
Let me distinguish different complexities. Loser complexity is the complexity of the loser's moves. Winner complexity is the complexity of the winner's moves.
Then in Uri's composition
[d]k7/P3p3/1q2Pp2/K1p1pP2/1pPpPp2/1P1P1P2/B7/b7 w - - 2 1
(#11 with a single path for the winner)
the loser complexity is high, but the winner complexity is only 1.
In the position
[d]3k4/8/3K4/3R4/3p4/8/8/8 w - - 0 1
loser complexity = winner complexity = 2.
In general
Winner complexity must be less than or equal to loser complexity (because of the requirement of a single path).
If (loser complexity > 1) & (winner complexity = 1),
then the loser's moves are irrelevant to the winner -- he plays the same moves regardless.
Let me distinguish different complexities. Loser complexity is the complexity of the loser's moves. Winner complexity is the complexity of the winner's moves.
Then in Uri's composition
[d]k7/P3p3/1q2Pp2/K1p1pP2/1pPpPp2/1P1P1P2/B7/b7 w - - 2 1
(#11 with a single path for the winner)
the loser complexity is high, but the winner complexity is only 1.
In the position
[d]3k4/8/3K4/3R4/3p4/8/8/8 w - - 0 1
loser complexity = winner complexity = 2.
In general
Winner complexity must be less than or equal to loser complexity (because of the requirement of a single path).
If (loser complexity > 1) & (winner complexity = 1),
then the loser's moves are irrelevant to the winner -- he plays the same moves regardless.
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Re: what is the longest tablebase mate with special properties?
It seems problemists call single-path problems "dual-free", so I'll switch to that terminology.
What I'd like to see is dual-free mates with high winner complexity (at least greater than 1, but greater than 2 would be better still).
What I'd like to see is dual-free mates with high winner complexity (at least greater than 1, but greater than 2 would be better still).
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Re: what is the longest tablebase mate with special properties?
[d]3k4/8/3K4/3R4/3p3r/6P1/8/8 w - - 0 1
Mate in 6, dual-free (with best play only),
winner complexity = 2.
1. gxh4 Ke8 2. Ke6 Kf8 3. Kf6 Kg8 4. Rxd4
Any deviation so far by White (Black) allows slower (faster) mate.
But now Black has a choice:
a) 4. ... Kh7 5. Rd8 Kh6 6. Rh8#
b) 4. ... Kh8 5. Kg6 Kg8 6. Rd8#.
Mate in 6, dual-free (with best play only),
winner complexity = 2.
1. gxh4 Ke8 2. Ke6 Kf8 3. Kf6 Kg8 4. Rxd4
Any deviation so far by White (Black) allows slower (faster) mate.
But now Black has a choice:
a) 4. ... Kh7 5. Rd8 Kh6 6. Rh8#
b) 4. ... Kh8 5. Kg6 Kg8 6. Rd8#.