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BGonline.org Forums
* * * Rollout, Surprise and Mystery... * * *
Posted By: Daniel Murphy In Response To: * * * Rollout, Surprise and Mystery... * * * (Klaus Evers)
Date: Thursday, 17 January 2008, at 3:11 a.m.
To illustrate what's happening with a rollout's presentation of the cubeless game breakdowns and the cubeless and cubefull equities, here is the line from the rollout for Redouble/Take after 3/off 2/off and a fan:
Player White owns 4-cube 0.736 0.000 0.000 - 0.264 0.000 0.000 +0.943 +0.792
Blue wins 73.6% and loses 26.4%. But that's cubeless. We can see that it's cubeless because 0.736-0.264 = 0.472, and 0.472 times 2 (since White is doubling) = 0.943 (more or less!). And 0.943 is Blue's cubeless equity. But Blue's cubeful equity is only 0.792. That's partly because White wins the majority of his redouble/takes to 8, and partly (it would be most unusual if it never happened) because White wins some games with a redouble to 8 that is passed.
Since we can't tell from the rollout how often White redoubles to 8, or how often that redouble is taken or passed, we can't tell exactly how many games Blue really wins after redoubling to 4. But by adjusting the cubeful equity for cube value we can say that Blue wins not 73.6% but the equivalent of 69.8%, since 0.698 - 0.302 = 0.396, and 0.396 * 2 = 0.792.
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