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Re: [Bug-gnubg] Results from the bot shootout

From: Joseph Heled
Subject: Re: [Bug-gnubg] Results from the bot shootout
Date: Thu, 5 Jul 2007 22:10:02 +1200

Even if gnubg wins a match only 49.5%, in a set of 1000 matches there
is more than 5% chance that gnubg wins 519 of them. that what 95% (one
sided) confidence interval means.


On 7/5/07, Achim Mueller <address@hidden> wrote:
* Joseph Heled <address@hidden> [070705 11:14]:
> With gnubg/Jelly we have p = .593 (estimated win percentage) and N =
> 1000. The 95%  confidence interval is [.562,.623], so we can be sure
> gnubg is better.
> gnubg/bgb p=.519 and the interval is [.487,.55] so you can't say gnubg
> is better than any of the others.

I understand your calculation, but what is wrong with mine? I took the
binominal distribution and my numbers seem to be correct, aren't they?

sqrt(519*481/1000) = sqrt(249,639) = 15.799

actual result(+38)/sigma(15.799) = 2.4 (oops, in my first calculation I
took +36, damn).

2.4 ---> 99.18% confidence that the same set of 1000 25p matches will
produce a win for gnubg. Ok, I miscalculated it, but this is even more
in favour of gnubg.



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