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World's incorrect 14-away/8-away pass: Analysis

Posted By: Timothy Chow
Date: Wednesday, 14 April 2010, at 12:50 a.m.

In Response To: World's incorrect 14-away/8-away pass: Analysis (Matt Cohn-Geier)

MCG wrote:

My point is that recube vig is independent of whether a recube is taken or dropped.

O.K., I guess my usage of the term "recube vig" isn't quite lining up with standard usage. Let me try to rephrase my points in a way that avoids this confusion.

Mathematically, you can take if

wins + (effective gammon wins)*(gammon price) – (effective gammon losses)*(gammon price)

equals or exceeds your raw takepoint. (Here wins include redouble/drop, and I'm assuming backgammons and re-recubes can be ignored.) This is just a mathematical fact. Any other method of deciding whether to take is just going to be some way of mathematically repackaging the above formula. One way or another, to get an accurate decision, you'll need to have some idea of how often you can recube, how often you'll get a take, and how often you'll win after that.

Now, in many positions, you can take a shortcut. This is the traditional approach to "recube vig." You get upper and lower bounds, and then you guess that the actual "recube vig" in this position puts you at some point in the middle. If this works, then all is right with the world.

The trouble is that this shortcut doesn't always work. This whole thread is sparked by a difficult case where the shortcut didn't work. So what do we do? Throw up our hands? I'm saying that we can do better. Go back to the basic mathematical formula. Use whatever intuition we have about the position to estimate effective gammons. Yes, this is an unfamiliar process. Yes, it is unnecessarily complicated for many "easy" positions. But (1) if you can make those estimates, then your calculation will be more accurate; (2) the calculation itself is not any more difficult than the usual calculation; (3) by breaking down the "recube vig" into its consituent components, we pave the way for pinpointing exactly what we do and don't understand about the position.

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