I was playing Blue against XG here. I thought this looked like a drop for money. At 5a7a, I would not have turned the cube in such a gammonish position, but, like Turz, I didn't think that at 6a7a the score would make enough difference to make me hold the cube. So I sent it over without doing any match-equity arithmetic.
The rollouts below show that I underestimated the effect of the score. According to the rollouts, this is a clear drop for money but an even clearer take ATS, and perhaps not even a double. To see why this is so, let's begin by noting that White could almost take even if she were to vow to redouble immediately regardless of my roll, because in this hypothetical scenario, she would need 30% game-winning chances and gammons wouldn't matter. Since in reality she doesn't have to redouble immediately, her chances are better than that, and the take is big.
From Blue's point of view, a redouble diminishes the value of his gammons, and since a sizable fraction of his equity comes from gammons, he should be cautious about turning the cube. It's similar to "Stick's rule" (though less pronounced). If things go poorly for Blue then White will still be able to take, and if things go well then often he will have even better gammon chances and will want his gammon value elevated rather than diminished.
Rollout ATS:
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| XGID=bB--C-B-B-A--BA--dAe-Ab-b-:1:1:1:00:1:0:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 70.66% (G: 28.65% B: 0.96%) |
| Opponent Winning Chances: | 29.34% (G: 8.79% B: 0.70%) |
| Double/Take | |
| Player Winning Chances: | 71.01% (G: 29.55% B: 1.60%) |
| Opponent Winning Chances: | 28.99% (G: 9.54% B: 0.91%) |
| Cubeless Equities | |
| No Redouble: | +0.626 |
| Redouble: | +1.008 |
| Cubeful Equities | |
| No Redouble: | +0.791 |
| Redouble/Take: | +0.787 (-0.005) |
| Redouble/Drop: | +1.000 (+0.209) |
| Best Cube action: No Redouble / Take | |
| Rollout details | |
| 2592 Games rolled with Variance Reduction. Dice Seed: 2 First 4 moves: 3 ply, cube decisions: 4 ply Remaining moves and Cube Decisions: 3 ply | |
| Confidence No Redouble: | ± 0.008 (+0.783...+0.800) |
| Confidence Redouble: | ± 0.013 (+0.774...+0.799) |
| Double Decision confidence: | 73.1% |
| Take Decision confidence: | 100.0% |
| Duration: 8 hours 27 minutes | |
eXtreme Gammon Version: 1.21, MET: Rockwell-Kazaross
Rollout for money:
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| XGID=bB--C-B-B-A--BA--dAe-Ab-b-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 70.46% (G: 28.98% B: 0.65%) |
| Opponent Winning Chances: | 29.54% (G: 8.66% B: 0.58%) |
| Double/Take | |
| Player Winning Chances: | 70.74% (G: 32.33% B: 0.60%) |
| Opponent Winning Chances: | 29.26% (G: 9.73% B: 0.93%) |
| Cubeless Equities | |
| No Redouble: | +0.613 |
| Redouble: | +1.275 |
| Cubeful Equities | |
| No Redouble: | +0.879 (-0.121) |
| Redouble/Take: | +1.095 (+0.095) |
| Redouble/Drop: | +1.000 |
| Best Cube action: Redouble / Drop | |
| Rollout details | |
| 2057 Games rolled with Variance Reduction. Dice Seed: 2 First 4 moves: 3 ply, cube decisions: 4 ply Remaining moves and Cube Decisions: 3 ply | |
| Confidence No Redouble: | ± 0.011 (+0.867...+0.890) |
| Confidence Redouble: | ± 0.017 (+1.078...+1.112) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 7 hours 09 minutes | |
eXtreme Gammon Version: 1.21