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## RE: [Bug-gnubg] real match winning chances

 From: Misja Alma Subject: RE: [Bug-gnubg] real match winning chances Date: Sat, 06 Dec 2003 21:48:20 +0100

```I read the article, interesting, I had never thought about this!
But also this luck rate is accumulated per move in updateStatContext. So it
could also accumulate up to a luck adjusted result of over 100%.
In fact the total after one match should be exactly the same as the
matchresult minus the added up unnormalized error totals of both players, or
do I miss something?

So I still would like to calculate either the luck adjusted result or the
error rate by multiplying my winning chance by (1- error) every time...

You asked why this would be right; It is not a mathematical proof, but I
think it's because of this:
When both players start a match both have 50% chance. Suppose I make an
error which should cost me half my match winning chances, then I will have
.5 * 50% is 25% mwc left. If a second situation comes up where I again blow
away half my match winning chances, then I might have comen back in the
match so at that point I have more than 25%. Or I might have fallen more
behind, but on average I should still have 25% mwc at that point (Assuming
that my opponent does not make any mistake). So my second error will cost me
.5 * 25% leaving me 12.5 % mwc. Etcetera.

Finally I agree that an analysis will always give a biased result towards
gnubg itself. But I think that when I analyze a match between me and another
human, this bias does not favour either of us.

Misja

-----Oorspronkelijk bericht-----
Verzonden: Saturday, December 06, 2003 9:11 PM
Aan: Misja Alma
Onderwerp: Re: [Bug-gnubg] real match winning chances

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%.

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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