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TG at -2, -2

Posted By: Daniel Murphy
Date: Wednesday, 22 October 2008, at 2:09 a.m.

In Response To: TG at -2, -2 (Matt Cohn-Geier)

Gnubg's evaluation of 52.88% wins is way off. But its evaluation of Blue's No Double MWC is pretty close, I think, and the recommended cube action of No Double is correct.

Gnubg estimates that ND equity is 53.07%. I figure Blue's No Double equity = 30.55% * 100% + 69.45% * 31.85% = 52.66%. (If Blue rolls a 6, he wins 30.55% and all wins are gammons. If he doesn't roll a 6, White doubles Blue out -- Gnubg's estimate that White would win only 30% and have no double is way off.)

Gnubg estimates that D/T equity is 52.88%. That's terrible. I figure Blue/s D/T equity at best = 30.55% + 69.45% * 10% = 37.5%. (I"m assuming that after Blue doesn't roll a six, an expert human player for White will not lose more than 10% of the time.)

So, Blue should not double, despite the existence of market losers. The match equity Blue obtains from rolling a 6 is 30.55% whether he doubles or not, but the match equity Blue obtains from not rolling a 6 is 31.85% if he doesn't double, and only 6.94% if he does.

But does this constructed position satisfy the proviso that E.g., no market losing sequence ever appears, but eventually one side rolls something that lets him become TG or TG/T or some such? How could Blue have reached this position without White (or Blue) ever having a proper double?

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