Author: Christophe Theron
Date: 17:31:07 10/09/01
Go up one level in this thread
On October 09, 2001 at 09:54:54, K. Burcham wrote:
>
>below is a response that was made to one of my posts.
>this was a mate in 11 that i got with the same program.
>i was unsure about the results because none of my other programs
>could find this mate in 11.
>now rex also has found this mate in 11. so i assume this is
>a true mate in 11.
>
>now the original question that i had. i also got this same eval,
>tiger shows a mate in 11, but could not see the mate until depth 16,
>and this was about an hour after depth 11, on a 1500 mhz.
>could you explain how the search works to get these results. in other
>words after a program advances its search to say a depth 12 , is it
>also still searching each ply below this even though it may have posted a depth
>12 result.
>so in this case when tiger posted the depth 15 level results, at that time
>was tiger also expanding the depth 11 search beyond its original post at depth
>11.
>also can we say that no matter what depth has been posted, a program can anounce
>a mate in ? (any lower level of its search) at any time.
>
>kburcham
>
>
>
>Here are the results running GT2 on a T-Bird 1.533Ghz.
>
>Finds mate in about 59 minutes
>
>Rex
>
>
>00:00:00.2 8.54 9 181024 Qc3 Qd7 Bxf6 Qd1+
>00:00:00.1 9.44 10 215587 Qc3
>00:00:00.1 10.26 10 251555 Qc3 Qd7 Bxf6 Qd1+
>00:00:02.7 14.46 10 1221735 Qf3 Qc7 Bh4 Qd7
>00:00:02.5 14.46 11 1233691 Qf3 Qc7
>00:00:03.5 15.36 12 1480027 Qf3
>00:00:04.9 15.36 13 2203372 Qf3
>00:00:06.5 16.26 13 2872472 Qf3
>00:00:31.9 25.43 13 14732114 Qf3 Qc7 Bh4 Qd7
>00:01:08.0 25.54 14 31975360 Qf3 Qd7 Bh4 Ka7
>00:03:26.8 26.33 14 96402848 Qd3
>00:22:51.7 26.80 14 672202266 Qd3 Kc7 Qd5 Qb6
>00:23:48.8 27.70 15 700424875 Qd3
>00:25:38.0 34.74 15 756108965 Qd3 Kc7 Qd5 Qb6
>00:30:46.9 35.64 16 898669765 Qd3
>00:59:08.4 Mate in 11 16 1808739336 Qd3 Kc7 Qd5 Qb6
>
>Here are the results running GT2 on a T-Bird 1.533Ghz.
>
>Finds mate in about 59 minutes
>
>Rex
>
> [D] 7b/q7/Pk3p1P/1Pp2pB1/K1P2P2/1Q6/8/8 w - - 0 1
Like Sven, I'm not sure I understand every word of your question, but I think I
understand its general meaning.
First of all, you seem to be mixing up "plies" and "moves". A mate in 2 moves
for example is a 3 plies long sequence:
a: first move by mating side
b: first move by opponent
c: second move, which is the mate, by mating side
a, b and c are "plies".
A mate in 3 moves is a 5 plies long sequence, and so on... A mate in X is a
2*X-1 plies
sequence.
A mate in 11 is a 21 plies sequence.
Second, the search depth displayed by a chess program gives you *no guarantee*
about the depth of the combinations or forced mate it can see.
Only a brute force chess program or a mate solver could give you some guarantee
about this: a guarantee of the highest ply depth at which it will find a forced
mate (a higher bound of the ply depth needed to solve the mate if you prefer).
But because of extensions the program could find the solution earlier anyway.
But all current top chess programs use a selective approach. Searching 10 plies
deep gives absolutely no guarantee that all possibilities on the next 5 moves
(=10 plies) are going to be seen by the program.
If you have a mate in X position, it is probable that my program will find it in
2*(X-1) plies, but in many cases it will find it in 2*(X-2) or 2*(X-3) plies
(solution found earlier because of extensions), and in some cases it might need
2*(X+10) plies or it might even NEVER find it.
The number of plies needed to solve a given mate in X is not fixed. It's like a
probability function. Here is a drawing of how it could look like for a large
sample of mate in 3 problems:
|
|
|
| .
| * * *
| * * * * * .
| * * * * * * * * . . .
+-------------------------------> search depth (plies)
1 2 3 4 5 6 7 8 9
The height of the columns represents the percentage of the sample positions
solved at a given ply depth.
Christophe
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