Re: [Bug-gnubg] real match winning chances

[Joern Thyssen]

On Sat, Dec 06, 2003 at 10:33:27PM +0100, Misja Alma wrote
> 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.

Don't you mean -50%? final-initial=50% and netluck=100%.

Anyway, I'm starting to understand you :-)

netskill = -50% => 0% MWC derives from assuming that player 1 starts out
at 0% instead of 50% since his net skill is -50%. As you correctly point
out, the changes in MWC occur in discrete steps, so there is a non-zero
chance that player 1 might get so lucky that he actually wins despite
his skill being -50%. 

I'm not sure how to model this mathematically?!  I'm also wondering if
it's possible to have a net skill of zero?

Douglas (CC'ed), can you comment on this?

Jørn

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