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Daniel Shawul

Joined: 14 Mar 2006
Posts: 2186
Location: Ethiopia

Post subject: Re: Perft(13) betting pool    Posted: Mon Jul 25, 2011 1:30 pm

hgm wrote:
Daniel Shawul wrote:
No, the point is when you do random move picking the probability you assigned to the moves can only be respected only at _inifinite_ number of games. Until then the estimate will hinge on the fact that how representative a move is picked up in my case (since I use constant multiplier), but in your case it requires perfect estimation of multipliers so it can give bad results.
 Quote: Again, not true. In my / Michel's method there is no estimation of multipliers at all. They are_calculated_ as 1/p_i, and the p_i, and I know exactly which p_i I am using to select the moves. The only thing I do not know is the x_i, so I do not know if the p_i I amusing are the optimal p_i.

[qutoe]
In your method, OTOH, you are dependent on representative moves being picked, while you biased the picking against that, so that the more often you pick, the less likely it will be that the picking will be representative. Only by having detailed advance knowledge of the sub-tree sizes, you can tweek things such that the non-representative picking happens to have the same mean as the value you are after.

In a Monte-carlo simulation you probably never revisit that same node again unless you do a lot of them. The multipliers are dependent on the probablity, which is dependent on sub-tree sizes. Your weights give more priority to the variance than the mean at fixed number of iterations. I prefer to use a simplistic heuristic like picking the middle move (as in LMR example) and multiply by the number of legal moves. If we do a single MC game, I would pick the middle moves at each ply and multiply by number of legal moves, which is a simple heuristic.But you have to determine weights appropriate for each ply depending on sub-tree size.

In the LMR case I don't tweak anything I just pick moves in the middle more often. I don't try to estimate how much their nodes count will be unlike in your case. I know this will give me a biased estimate in the long run but with fixed number of games it can perform better.
In your case the heuristic has to be good very good to estimate the mean with fixed number of games because attention is shifted to reducing variance by allocating more weight to the nodes with bigger sub-trees.

Also when we do LMR perft the tree is tapered to the right. Like an inverted triangle. If you pick the first move and multiply by certain weight, you are _assuming_ this pattern is going to repeat itself along the whole width of the tree within in the same ply. Which is clearly wrong. But my method tends to pick game paths towards the middle of the tree from top to bottom of the tree.
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Steven Edwards Sun Jul 10, 2011 3:29 pm
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Daniel Shawul Sun Jul 10, 2011 6:32 pm
H.G.Muller Sun Jul 10, 2011 6:48 pm
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Daniel Shawul Mon Jul 11, 2011 12:50 pm
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H.G.Muller Mon Jul 11, 2011 3:19 pm
Daniel Shawul Mon Jul 11, 2011 3:27 pm
Julien MARCEL Mon Jul 11, 2011 3:26 pm
Sven Schüle Mon Jul 11, 2011 4:42 pm
Daniel Shawul Mon Jul 11, 2011 4:53 pm
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Daniel Shawul Mon Jul 11, 2011 6:55 pm
Sven Schüle Mon Jul 11, 2011 7:04 pm
Daniel Shawul Mon Jul 11, 2011 7:09 pm
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H.G.Muller Mon Jul 11, 2011 7:54 pm
Daniel Shawul Mon Jul 11, 2011 9:12 pm
Julien MARCEL Mon Jul 11, 2011 4:59 pm
H.G.Muller Mon Jul 11, 2011 5:28 pm
Julien MARCEL Mon Jul 11, 2011 5:47 pm
Daniel Shawul Mon Jul 11, 2011 5:49 pm
Uri Blass Mon Jul 11, 2011 8:01 pm
Daniel Shawul Mon Jul 11, 2011 9:20 pm
H.G.Muller Mon Jul 11, 2011 9:27 pm
Daniel Shawul Mon Jul 11, 2011 9:33 pm
Adam Hair Sat Jul 16, 2011 9:43 am
Jesús Muñoz Wed Jul 20, 2011 4:44 pm
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Daniel Shawul Fri Jul 22, 2011 2:00 pm
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Daniel Shawul Fri Jul 22, 2011 3:47 pm
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Re: Perft(13) betting pool Daniel Shawul Mon Jul 25, 2011 1:30 pm
Michel Van den Bergh Tue Jul 26, 2011 7:02 am
Daniel Shawul Tue Jul 26, 2011 8:36 am
H.G.Muller Tue Jul 26, 2011 9:42 am
Sven Schüle Tue Jul 26, 2011 10:23 am
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H.G.Muller Tue Jul 26, 2011 11:02 am
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Michel Van den Bergh Tue Jul 26, 2011 3:07 pm
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H.G.Muller Sun Aug 07, 2011 5:38 pm
Daniel Shawul Sun Aug 07, 2011 6:41 pm
H.G.Muller Sun Aug 07, 2011 8:51 pm
Daniel Shawul Mon Aug 08, 2011 1:08 pm
Daniel Shawul Sun Aug 07, 2011 11:35 am
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Peter Österlund Mon Aug 08, 2011 5:49 pm
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Daniel Shawul Mon Aug 08, 2011 11:26 pm
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Michel Van den Bergh Fri Aug 12, 2011 11:49 pm
Michel Van den Bergh Wed Aug 10, 2011 2:08 pm
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Michel Van den Bergh Sat Aug 06, 2011 6:59 am
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Sven Schüle Tue Aug 09, 2011 6:35 pm
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Peter Österlund Mon Aug 15, 2011 6:35 pm
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Daniel Shawul Sat Aug 13, 2011 8:32 pm
Michel Van den Bergh Sat Aug 13, 2011 8:55 pm
Daniel Shawul Sat Aug 13, 2011 9:01 pm
Michel Van den Bergh Sat Aug 13, 2011 9:26 pm
Daniel Shawul Sat Aug 13, 2011 9:51 pm
Michel Van den Bergh Sat Aug 13, 2011 10:05 pm
Daniel Shawul Sat Aug 13, 2011 10:22 pm
Michel Van den Bergh Sat Aug 13, 2011 10:42 pm
Daniel Shawul Sat Aug 13, 2011 10:57 pm
Michel Van den Bergh Sat Aug 13, 2011 11:11 pm
Daniel Shawul Sat Aug 13, 2011 11:24 pm
Michel Van den Bergh Sat Aug 13, 2011 11:16 pm
Daniel Shawul Sat Aug 13, 2011 11:30 pm
Michel Van den Bergh Sun Aug 14, 2011 7:22 am
Michel Van den Bergh Sun Aug 14, 2011 8:32 am
Daniel Shawul Sun Aug 14, 2011 10:34 am
Michel Van den Bergh Sun Aug 14, 2011 10:45 am
Daniel Shawul Sun Aug 14, 2011 10:55 am
H.G.Muller Sat Aug 13, 2011 9:07 pm
Peter Österlund Sat Aug 13, 2011 9:56 pm
Michel Van den Bergh Wed Aug 17, 2011 4:44 am
Peter Österlund Wed Aug 17, 2011 5:20 am
Michel Van den Bergh Wed Aug 17, 2011 9:22 am
Michel Van den Bergh Wed Aug 17, 2011 10:41 am
Michel Van den Bergh Wed Aug 17, 2011 11:19 am
Michel Van den Bergh Wed Aug 17, 2011 11:53 am
Michel Van den Bergh Wed Aug 17, 2011 3:18 pm
Daniel Shawul Wed Aug 17, 2011 3:43 pm
Daniel Shawul Wed Aug 17, 2011 8:56 pm
Michel Van den Bergh Thu Aug 18, 2011 9:56 am
Daniel Shawul Thu Aug 18, 2011 3:51 pm
Daniel Shawul Fri Aug 19, 2011 2:25 pm
Michel Van den Bergh Sat Aug 13, 2011 9:58 pm
Peter Österlund Sun Aug 14, 2011 10:35 am
Michel Van den Bergh Sun Aug 14, 2011 10:42 am
Daniel Shawul Sat Aug 13, 2011 12:55 pm
Peter Österlund Sat Aug 13, 2011 2:14 pm
Michel Van den Bergh Sat Aug 13, 2011 2:41 pm
Peter Österlund Sat Aug 13, 2011 3:04 pm
Peter Österlund Sat Aug 13, 2011 7:08 pm
Daniel Shawul Mon Aug 15, 2011 1:17 pm
Peter Österlund Mon Aug 15, 2011 5:29 pm
ethan ara Mon Aug 15, 2011 6:31 pm
Daniel Shawul Mon Aug 15, 2011 8:12 pm
Daniel Shawul Tue Aug 16, 2011 2:36 am
Michel Van den Bergh Tue Aug 16, 2011 5:01 am
Michel Van den Bergh Tue Aug 16, 2011 5:33 am
Michel Van den Bergh Tue Aug 16, 2011 8:27 am
Daniel Shawul Tue Aug 16, 2011 11:07 am
Michel Van den Bergh Tue Aug 16, 2011 11:17 am
Michel Van den Bergh Tue Aug 16, 2011 11:19 am
Daniel Shawul Tue Aug 16, 2011 11:31 am
Michel Van den Bergh Tue Aug 16, 2011 11:49 am
Daniel Shawul Tue Aug 16, 2011 12:50 pm
Michel Van den Bergh Tue Aug 16, 2011 2:09 pm
Daniel Shawul Tue Aug 16, 2011 3:42 pm
Michel Van den Bergh Tue Aug 16, 2011 4:02 pm
Daniel Shawul Tue Aug 16, 2011 4:15 pm
Michel Van den Bergh Tue Aug 16, 2011 4:38 pm
Michel Van den Bergh Tue Aug 16, 2011 4:55 pm
Daniel Shawul Tue Aug 16, 2011 5:02 pm
Michel Van den Bergh Tue Aug 16, 2011 5:43 pm
Daniel Shawul Tue Aug 16, 2011 6:34 pm
Michel Van den Bergh Tue Aug 16, 2011 6:38 pm
Daniel Shawul Tue Aug 16, 2011 6:56 pm
Michel Van den Bergh Tue Aug 16, 2011 9:02 pm
Daniel Shawul Sat Aug 20, 2011 2:45 pm
Daniel Shawul Tue Aug 16, 2011 4:04 pm
Michel Van den Bergh Tue Aug 16, 2011 4:14 pm
Daniel Shawul Tue Aug 16, 2011 4:22 pm
Daniel Shawul Tue Aug 16, 2011 5:21 pm
Daniel Shawul Tue Aug 16, 2011 5:40 pm
Daniel Shawul Tue Aug 16, 2011 7:32 pm
Daniel Shawul Tue Aug 16, 2011 10:53 am
Michel Van den Bergh Tue Aug 16, 2011 11:07 am
Daniel Shawul Tue Aug 16, 2011 11:10 am
Steven Edwards Mon Aug 15, 2011 5:41 am
Michel Van den Bergh Mon Aug 15, 2011 9:27 am
Sven Schüle Mon Aug 15, 2011 11:13 am
Sven Schüle Mon Aug 15, 2011 12:42 pm
Sven Schüle Mon Aug 15, 2011 2:08 pm
Michel Van den Bergh Mon Aug 15, 2011 2:31 pm
Sven Schüle Mon Aug 15, 2011 3:12 pm
Michel Van den Bergh Mon Aug 15, 2011 3:29 pm
Sven Schüle Mon Aug 15, 2011 3:51 pm
Steven Edwards Mon Aug 15, 2011 12:47 pm
Daniel Shawul Mon Aug 15, 2011 1:32 pm
Steven Edwards Mon Aug 15, 2011 2:32 pm
Peter Österlund Mon Aug 15, 2011 6:13 pm
Steven Edwards Wed Aug 17, 2011 6:11 am
Steven Edwards Wed Aug 17, 2011 4:37 pm
Steven Edwards Fri Aug 19, 2011 7:37 pm
Steven Edwards Tue Aug 23, 2011 10:04 pm

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