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RO surprise: winning the most games AND most gammons is not the best move...?!

Posted By: Daniel Murphy
Date: Sunday, 13 May 2012, at 4:20 p.m.

In Response To: RO surprise: winning the most games AND most gammons is not the best move...?! (Bob Koca)

As a rough estimate (I may have more bot-assisted numbers later):

6/3 6/2 -> (60% * 2 points) + (10% * 4 points) - (28% * 2 points) - (2% * 4 points) = 1.2 + 0.4 - 0.56 - 0.08 = 0.960 money game equity. This is assuming that you always have a double/take next turn which I think is true but need to verify with Gnubg, which does not evaluate this position well.

9/5*/2 -> you either get hit, or just have the one outside blot to clear. After the 31/36 nonhitting returns you have double/pass next turn. Entering with a nonhitting ace is not good enough for White. So far so good -- for those 31/36 sequences only, 86% * 1 point = 0.860 money game equity is better than about 86% * ((60% * 2 points) + (10% * 4 points) - (28% * 2 points) - (2% * 4 points)) = 0.826. In other words, even though your double-in is very good after 6/3 6/2, you'd still rather cash those 31/36 games, having played 9/5*/2.

The problem is the other 5/36 games. You've lost your double/take and you're an underdog to win. These sequences are far from hopeless -- you're a favorite to enter and hit a home board blot (but you might expose a second blot, and you still have to bring your last blot home) and White will have 3, 4 or 5 other blots, so you might win about 40% of them -- so your money game equity should be about (for simplicity I'll just assume that all the games after a hit are cashed by one side or the other) (91% * 1) - (9% * 1) = 0.820.

In short, with the centered cube you'd rather play 6/3 6/2 and double White in every time next roll, winning about 60% single games and 10% gammons cubeful, then play 9/5*/2 even though you'd win about 91% of the time cubeful after 9/5*/2.

Also, note how misleading the "cubeless" numbers in the ATS rollout might be: cubeful, 9/5*/2 wins about 20% more games than 6/3 6/2, not 2.27% more games, and wins far fewer doubled or undoubled gammons, perhaps about 2% cubeful, compared to about 10% after 6/3 6/2.

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