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Daniel Shawul

Joined: 14 Mar 2006
Posts: 2187
Location: Ethiopia

Post subject: Re: Perft(13) betting pool    Posted: Fri Jul 15, 2011 2:02 pm

 Quote: The question is if we can use these sequences to have an unbiased estimate for perft(13) E(p(1)*p(2)*p(3)*p(4)...*p(13)) or in the specific case the derived claim is that sum of perft(3) values of (p(4)*...p(13) for all the possible first 3 plies) is a variable that get expected value of perft(13) and we can use many samples to get a good estimate for the standard deviation of it. Note that I found that the expected value of the multiplication on a random game is a biased estimate but practically we do not generate a random game by generating random moves and it seems at least based on one example that I tried that it is unbiased estimate but we need to prove it.

I haven't looked into your method Or peter's proof carefully but you are saying your estimate is biased? If p(1),p(2)..p(n) are all independent then E(XYZ..) = E(X)E(Y)... . Does the proof by induction proof that this relation remains valid even for perft(13) when we have dependent p(i) values ? I am just beginning to look at the proof so excuse my late jump in...
Edit: My doubt is if your estimate is biased ,i.e the one you get by doing random games, this one should also be biased because we are doing unfinished games of 13 ply.
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Re: Perft(13) betting pool Daniel Shawul Fri Jul 15, 2011 2:02 pm
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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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