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Giving Up Equity to Get More Back

Posted By: Casper Van der Tak
Date: Tuesday, 16 August 2016, at 12:09 p.m.

In Response To: Giving Up Equity to Get More Back (Maik Stiebler)

I think that Dimitriy's point is helpful and probably under appreciated by a lot of people (not by you - I believe you are a mathematician right). For simplicity, put all checkers on the ace for both sides, 8 checkers against 8. Centered cube as before. If someone takes 3-roll vs 3-roll, but not 2-roll against 2-roll, should you double now?

Per Dimitriy, we can ignore non-double vs non-double as irrelevant. Not doubling gains on ND followed by D, or 5/36 of the time. Gain is 5/36 * 0.722 is 0.100. Not doubling loses on D followed by any roll, 1/6 of the time. Loss on these sequences is 1/6 * 196/216 = -0.151 As losses from not doubling are larger than the gains, you ought to double.

This is a relatively easy calculation facilitated by focusing on the sequences where delaying the cube matters.

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