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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 22:33:27 +0100

Sorry, I think I didn't express very clearly what I meant, the example I
gave could be more complete. Here is my explanation again:
So 2 players start a match, and at that point both have 50% chance.
When player 1 makes a mistake which costs him half his mwc, this costs him
.5 * 50% = 25% mwc. Gnubg will find this also.
But now let's assume that the player gets lucky and comes back to 50% mwc
again. At that point he makes again a mistake which costs him half his mwc;
so 25%. What gnubg does is it addes up error1 and error2, for a total of
50%. If these were all the errors both players made this match, it will then
estimate player 1 to have 0% mwc in an analysis.
The luck rate will do something similar: After his first error player 1 must
have had luck worth for 25% mwc. Suppose that player1 won the match anyway
after his second mistake, he must have had another portion of luck worth for
75% mwc this time. Both are added up for a total of 100%. final - initial =
netLuck + netSkill; Filling the numbers in gives that netSkill must be zero.

Btw I checked this by playing a 1pt match against gnubg with manual dice,
where I tried to make all possible errors but gave gnubg such poor dice that
it lost anyway; An analysis gives me a total error rate of -128% and a luck
adjusted result of -137%.

I think that those numbers are not right. If I would do a prediction of the
mwc of player 1 against player 2 based only on the match above, I would say
that player 1 apparently gives away half his mwc twice during a match,
regardless of what the situation or matchscore is at those times. So his mwc
will be on average 50% * .5 *.5 = 12.5%.


-----Oorspronkelijk bericht-----
Van: address@hidden
[mailto:address@hidden Joern Thyssen
Verzonden: Saturday, December 06, 2003 10:00 PM
Aan: Misja Alma
CC: address@hidden
Onderwerp: Re: [Bug-gnubg] real match winning chances

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
> 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,
> 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
> 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.


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