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> As we are currently aware, the Woolsey 22% gammon rate
> remains static across all match lengths.
Not exactly. Kit Woolsey has written in this newsgroup some remarks
that bear on this and on your inquiry overall:
[Quotes from Kit Woolsey on aspects of how Woolsey MET was created:]
********************************************
I will be the first to admit that there may be errors in my table. The
figures were not derived on a particularly scientific basis. There are
a mishmash of empirical data, a program which was based on some
assumptions which may not be sound, a lot of judgment, and some
fudging. Other people have derived similar match equity tables, all of
which are probably just as inaccurate.
First of all, let's see what we mean by gammon rate. If there is a
possibility that the game may end with a cube turn then gammon rate
really doesn't mean all that much. So, we are only looking at games
which must be played to conclusion -- and this can happen only at
Crawford or at Post-Crawford scores. Under these circumstances,
depending on the score, either the gammon will be of great value to one
side or it will be of no value to anybody.
Thus, it is clear that a change in the estimated gammon rate would only
have a major effect on Crawford and Post-Crawford equities. For other
scores the gammon rate would have less effect, decreasing as we got
farther away from the Crawford game. Thus the above claim that the
equity changes from 58% to 63% on the 12 away 14 away score as the
gammon rate changes is clearly wrong -- a change in the gammon rate
will have very little affect for that score.
When I first constructed my equity table I believe I used a gammon rate
of about 21%. This was consistent with my own estimates as well as the
results from a data base of several hundred games which had to be
played to conclusion due to the match score. Currently I think the
theoretically correct figure should be higher, perhaps 25%, with
correct play. However since most players are not sufficiently adept at
gammon collection the 21% figure appears to work out well in practice,
and the match equity table is consistent with real life results.
Personally I consider Friedman's 36% estimate way out to lunch. He has
no evidence to back this up other than his own, probably biased,
rollouts. All three computer programs (Expert Backgammon, TD-Gammon,
and Jellyfish) come up with a gammon rate somewhere in the mid 20's,
and this would be what the majority of experts would agree with also, I
think.
Keep in mind that I did not construct my equity table using a precise
formula. Rather, I took a large data base of empirical results, molded
together some assumptions from these results, did the appropriate
fudging, and out came my match equity table. I don't claim it is
mathematically precise, but it does have one very important thing going
for it -- it appears to work!
When I first tried constructing a match equity table (about 15 years
ago), I also had the equity for 12 away, 14 away higher than the 58% I
have now. What happened was that I did not give sufficient weight to
the trailer's cube leverage at different match scores, so in general I
kept coming up with the leader having more of an advantage than he
actually had in real life. I believe Robertie made the same error,
which is why his table in Genud vs. Dwek is different from mine. I
still don't know how to express this cube leverage in mathematical
terms -- perhaps someone who can find an accurate way to do so can come
up with a better table. However, I do believe that my table does
properly represent the cube leverage the trailer has in real life.
********************************************
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