I wasn't going to answer this one but since king fish Iancho did I'll go ahead and put out my 2 cents worth also.
First, our opponent's take point:
- Double/Pass for -10 -3 or 13%
- Double/Take/Lose for -10 -1 C or 4%
- Double/Take/win for -6 -5 or 43%
We are risking 9% (13-4) to gain 29% (43-13) and our take point is equal to risk/(risk+gain) or 9/(9+29) >> 9/38 or ~23.5% as our raw take point. Truth be told I don't think we get a hell of a lot of cube leverage here out of owning the cube so I wouldn't add much on to our raw take point for that. However, we still slime a couple gammons in positions like this, let's call it 2%, and our gammon value on a 4 cube would be high, .8. This lowers our take point to 22%. Add a little cube vig in if you like and shoot with 20% as our fully adjusted take point.
Now that we know what our opponent needs to take, does he have it and if so by how much because the position is pretty volatile. We may be lucky enough to know the reference position below which is close to what we hope to achieve. There are two points of difference in the actual position which I will say cancel out each other from the reference position. In the actual position we aren't likely at all to achieve a perfect spare distribution. Our opponent's position is also worse off by not having a perfectly crunched two point board with a decent spare distribution. Truthfully the non perfect crunch probably hurts more than the spare distribution but in situations like this I keep that in the back of my head if it ends up being close and don't factor it in immediately because it doesn't have much of an impact on the position.
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| XGID=aBBBCCB--A-------------ef-:1:-1:1:21:0:0:3:0:10 | ||||
 to play 21 | ||||
is Player 1| 1. | Rollout1 | 9/6 | eq: +0.765 | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: 21140344 Moves and cube decisions: 3 ply | ||||||
So if we close our opponent out he will still maintain 10% game winning chances. How often do we close him out on the immediate sequence? All 2s, 7s, 10s, and one 12 cover. [11 21 22 32 42 52 62 43 61 64 55 66] That's 21 rolls. That means we cover immediately about 59% of the time and from there our opponent only wins 10% of the games. So out of the 21 games when we cover we win ~19 of them or ~53% of the total games..
What of the remaining 15 games? When we don't cover all is not lost, especially since because of our opponent's funk position when he enters with 31 or 32 he cracks and leaves even more blots lying around for us to pick up. These are barely better than fanning and 33 doesn't get him out of the house so really he only has 6.5 good rolls when we don't cover. Our opponent is also favored to fan. Let's say our opponent wins just over 1/6th of these games, the same amount of good rolls he has when we fail to cover. That's about 3 more games or in total he wins 5 games out of 36 or ~14%.
If he only wins 14% there is no way I can hold on to the cube here. This is a must double. Unless I've misjudged the recube vig here you have to let this go. It's hard to get an estimate on how often the 8 cube will be tossed out and have value here.
Stick