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BGonline.org Forums
More than a MET
Posted By: Fabrice Liardet
Date: Tuesday, 23 June 2009, at 2:55 p.m.
I would like to know what is the probability distribution of the distinct possible results, at various scores and for money ("distinct" in the sense that winning 4 or 8 points is equivalent when less than 4 away). I don't think it can be worked out from a MET ; for instance, I can't even determine who wins more games at pure gammon-go.
Have those distributions been worked out with rollouts ? Or how would I be able to work them out with my own GNU rollouts ?
Side note :
The utility I see for those probability distributions is that it would allow to normalize each score in the sense that one could play repeated games at the same score, while keeping track on the aggregate result in terms that are comparable with DMP games or match play (where the average deviation is 1 if one counts wins as 1 and losses as -1). That would even allow to define such a thing as a GG or a money game Elo rating.
Example :
If I suppose that each player wins exactly 50% of the games at pure gammon-go (-2,-1 Crawford), then it means that 50% of the games are won by the GS player, about 36% are single wins for the GG player and about 14% are gammon wins for the GG player - that is the distribution and can be worked out from the (-2,-1) MET value. Then you can also check that granting 1 point for each of GS's wins, about 0.56 point for each of GG's single wins and about 2.125 points for each of GG's gammons has the desired property that the equity is 0 and that the average deviation is 1.
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