Re: [Bug-gnubg] real match winning chances

[Joern Thyssen]

On Sat, Dec 06, 2003 at 08:54:36PM +0100, Misja Alma wrote
> Hi,
> 
> There is a feature which I would very much like to have, and that, as far as
> I can see, is not present in gnubg. That is that the 'real' match winning
> chance would be shown in the analysis output.
> With 'real' match winning chance I mean the chance I have against an
> opponent based on the errors we both have made in the match that was
> analyzed.
> Right now I can see the error rate, which is also given in percentages. But
> if I understand the code right then the error rate is calculated by
> accumulating all the errors. If this total results in a percentage above
> 100% or below zero it is truncated.
> I would like to have a percentage which is really between 0 and 100%.

It's already there :-) It's called "Luck adjusted result" calculated as
described in <URL:http://math.columbia.edu/~zare/vrskill.html>

The calculated quantity is mathematically guarenteed to be unbiased
towards any player (including the bot ifself). The theory behind "luck
adjusted results" is exactly the same as for variance reduction in
rollouts.

> The reason is that when I play for money on GamesGrid, I not only want to
> know if I was a favourite but also if I was enough of a favourite to
> compensate for the fee.
> I can't trust the percentage gnubg gives because it is biased towards the
> favourite, the same applies to Snowie( which sometimes really shows a match
> winning chance of over 100%..).
> 
> I think the real match winning chance should be calculated by starting with
> 50% and then multiplying it after every error  with (1 - ErrorPercentage).

Why? I can't see why this should be right.

Anyway, this algorithm would still lead to a biased result since
ErrorPercentage is always biased towards gnubg.

Jørn

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