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

[Joern Thyssen]

On Mon, Jun 09, 2003 at 07:14:08AM -0700, Rod Roark wrote
> As others mentioned, there's a square root involved in the
> calculation of standard deviation.  I believe there are a
> couple of different ideas in use as to the exact formula.
> 
> However I don't think you want this calculation anyway.  It
> is an attempt to answer the question "how much do the
> results differ from the average?".  Well if each result
> must be either 0 or 1 and the average is somewhere around
> 0.5, then they will all differ by 0.5.  This is not an
> interesting number.
> 
> The question to answer is, "how significant is the result
> from 100 matches?".  This depends in part on "how much does
> a match depend on skill, and how much on luck?".  The answer
> to that last question is elusive.

I know how to calculate the luck by analysing the matches and extracting
the total luck. 

The 95% confidence interval is calculated as 1.96 * std.dev. So with 100
matches and a final result of 56 wins to gnubg and std.dev of 0.5, I
get:

56% +/- 98%

What I don't understand is that if I had played 100000000000 matches and
gnubg won 54000000000 of them, I would still have a std.dev of 0.5, thus
I still get:

56% +/- 98%

So what did I get wrong?

Jørn