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What is the lowest winning % for Too good?

Posted By: ah_clem
Date: Sunday, 7 July 2013, at 12:32 p.m.

In Response To: What is the lowest winning % for Too good? (Matt Cohn-Geier)

If match play is OK, I can come up with positions that are TG with very low winning chances. I imagine it is continuous and so only positions with 0% winning chances or 0% gammon chances cannot be TG.

There are only finitely many positions of the 30 checkers. However, there are countably many cube values and countably many match scores, so the universe of possibilities is countable. It is not a continuum.

The question then becomes whether there is a sequence of points in this space that converges to 0 GWC while being TGTD. My hunch is no, since long match scores converge to money play. However large asymmetric match scores and correspondingly large cube values may converge in this manner - if so, it shouldn't be too hard to construct an example.

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