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## Re: [Bug-gnubg] Snowie 4 vs. GNU 0.13

 From: Joern Thyssen Subject: Re: [Bug-gnubg] Snowie 4 vs. GNU 0.13 Date: Mon, 9 Jun 2003 10:14:17 +0000 User-agent: Mutt/1.4.1i

```On Mon, Jun 09, 2003 at 12:12:23AM -0300, Albert Silver wrote
> Hi all,
>
>       This is just to report that the series of 100 7-point matches
> has finished and the final score was 56-44 in GNU's favor. Attached are
> the matches so that any may see them. Many thanks to Tony Lezard for his
> program that made the match-up possible, and of course a huge
> congratulations to the GNU team.

Can someone help me to calculate the std. deviation, please!

My idea was to calculate gnubg's average win, e.g.,

sum(i=1,100) result_i
p = ---------------------
100

where result_i=1 if gnubg won and result_i=0 if Snowie won.

The variance can be written as

variance=average(result^2) - ( average(result) ) ^2

However, as average(result^2) = average(result)=p then the variance can b
reduced to

variance=p-p^2

That, is /independent/ of the number of samples!

In this example I get

mean=0.56 and std. deviation=0.50, thus

gnubg wins 0.56 +/- 0.98

What am I doing wrong?

Jørn

```