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RE: [Bug-gnubg] real match winning chances

From: Misja Alma
Subject: RE: [Bug-gnubg] real match winning chances
Date: Sun, 07 Dec 2003 08:55:31 +0100

I agree with you that the luck adjusted result that gnubg is reporting right
now is also meaningful. Perhaps it would be possible to show both?

You have a good point there when you mention that over a large number of
matches the current luck adjusted result will average to the real mwc.
I was thinking about another possibility, right now gnubg analysis shows an
estimated FIBS rating. From what I've read this must be quite accurate.
Isn't it possible to calculate the mwc of player 1 vs player 2 based on both
their estimated FIBS ratings?


-----Oorspronkelijk bericht-----
Van: address@hidden
[mailto:address@hidden Christopher D.
Verzonden: Sunday, December 07, 2003 3:08 AM
Aan: Misja Alma; Joern Thyssen
CC: address@hidden
Onderwerp: RE: [Bug-gnubg] real match winning chances

At 10:33 PM 12/6/2003 +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
>estimate player 1 to have 0% mwc in an analysis.
>The luck rate will do something similar: After his first error player 1
>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
>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

For Player 1:

initial mwc = 50%, final mwc = 100%
netSkill = -50% (Player 1 gave up 50% mwc, Player 2 gave up 0% mwc in this
hypothetical example)
net luck = +100%
result = +50%

>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
>it lost anyway; An analysis gives me a total error rate of -128% and a luck
>adjusted result of -137%.

(Note: the total error rate = luck adjusted error rate if gnubg's match
analysis is perfect; since gnubg's match analysis is not perfect, the above
result seems reasonable.)

Suppose that Player A (playing perfectly) plays Player B (an extremely weak
player, e.g. a computer making all checker and cube decisions
randomly).  In general Player A is > 99.9999% favorite (let's round this to
100%).  However, if these matches are analyzed, sometimes Player A will get
very good dice and will quickly win the match.  In these matches, player B
won't have many opportunities to make errors and may only make, say, 25%
mwc worth of errors, resulting in a luck adjusted result of -25% mwc.  In
other matches though, Player B will get very good dice which will prolong
the match, giving him more opportunities to make errors.  In these matches
he might make, say, 75% mwc worth of errors, resulting in a luck adjusted
result of -75% mwc.

On average player B will make 50% mwc errors per match.  In a given match
he may make less than or more than 50% mwc worth of errors.  Player A's
expected result is +50% mwc (i.e. he expects to win 100% of the matches).

>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
>will be on average 50% * .5 *.5 = 12.5%.

I disagree.  In the extreme example that I gave, I'd be annoyed if gnubg
didn't report Player A's luck adjusted result as > +50% mwc in some of its
matches.  Gnubg is just reporting what happened in the individual match (I
like how it does it).

It's important to analyze a large number of matches.  What matters is the
average luck adjusted result.  In extreme examples, as I gave above, the
length of the match (which is positively correlated with Player B's net
luck) significantly affects the luck adjusted result of an individual match.


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