Re: [Bug-gnubg] real match winning chances

[Joern Thyssen]

On Sat, Dec 06, 2003 at 09:48:20PM +0100, Misja Alma wrote
> 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%.

Yes, but only because gnubg is an imperfect bot. 

> 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?

You're correct for a perfect bot, but gnubg is not.

Result = net luck + net skill

We're after net skill:

net skill = result - (net luck)

With a perfect bot you can either decide to calculate "net skill"
directory by summing up the unnormalised errors or you can decide to
calculate the "net luck". 

> 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%. 

I still don't understand this.

gnubg reports errors normalised to the match, so it would report the two
errors as costing 25% MWC and 12.5% MWC. I don't see the need for
multiplying as gnubg reports unnormalised luck and errors to the match
length and not relative to the current game.

Jørn

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