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Double/DoubleA New Variation
Posted By: Stein Kulseth
Date: Saturday, 14 September 2013, at 6:33 p.m.
In Response To: Double/DoubleA New Variation (Bob Koca)
After having done that one try checker on 1 and 4 vs 1 and 4.
 Double/drop
 Doubler's equity is oviously +2 (1 point each cube)
 No double
 The Doubler is 29/36 to win outright, and then 7/36 to win by his opponent failing to get off (and even with centered cube we have seen that opponent does not have a cube here). So Doubler's equity is (29/36 + 7/36 * (7/36  29/36) ) * 2 = +1.37
 Double/take/opt. take
 Again, a 4, 5 or 6 leaves the doubler gin, and the taker with an obvious 2nd cube drop, contributing 3/6 * 3 = +1.5 to the doubler's equity.
And again, an ace leaves the Doubler even money to get off, and the Taker with an easy take, but now the Doubler has some additional chances even if he fails to get off. We have seen that ace+4pt vs 1roll has 1.22 equity not 2, so the Ace variation now contributes 3/6 * 4  3/6 * 22/36 * 4 = +0.78
 Note, the taker might choose to drop the 2nd cube, in order to have a cash with his single 1st cube when the doubler fails to roll 4,5,6. This makes the 1st cube a wash, but at the cost of dropping the 2nd cube which would raise Doubler's equity to +1
Last, a 2 or 3 allows the Taker to beaver the last cube, but now it seems the Doubler can take the beaver (Although the rules aren't quite clear on what would be the 1st or 2nd cube when doubling with two cubes on different levels). This means that this variation contributes 2/6 * (1/6 * 6  5/6 * 22/36 * 6) = 0.69, for a total of +1.59So now it seems it is a proper double/take. No guarantee for correctness  things got confusing quickly here.
For completeness' sake, what would happen if I take the first cube and beaver the 2nd, and on my next turn doubles back?
Would I be able to designate which cube is the first, or is my opponent allowed to choose which one to take first?

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