Neil, Stick, and Dmitriy already explained what is going on. This is an excellent illustration of O'Hagan's rule in action. Any 6 by blue is a market loser, while there are two anti jockers in 44 and 33. The difference is 9 -- just enough for a double. Actually, you also need to look how the remaining rolls play to make sure you at least "break even" in those. We have two bad rolls that bury our spares deep -- 54 and 53 -- and three good rolls that don't break the prime -- 31, 21, and 11. So, we are doing OK on average in the non-jocker rolls and can double.
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| XGID=-bBBBBCB-----------cccbbB-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 61.08% (G:12.58% B:0.46%) | 61.40% (G:12.45% B:0.51%) |
| Opponent Winning Chances: | 38.92% (G:8.61% B:0.34%) | 38.60% (G:8.77% B:0.36%) |
| Cubeless Equities | +0.262 | +0.533 |
| Cubeful Equities | ||
| No double: | +0.253 (-0.019) | ±0.004 (+0.250..+0.257) |
| Double/Take: | +0.272 | ±0.006 (+0.266..+0.279) |
| Double/Pass: | +1.000 (+0.728) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Dice Seed: 1405227 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 24 minutes 44 seconds | ||
eXtreme Gammon Version: 2.10
Move our spare to the 5pt and instead of three good non-escaping rolls we are left with only one -- 21. We still have 54 and 53 and hence the non-jocker rolls are not quite in our favor. We are just short of a double.
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| XGID=-bBBBCBB-----------cccbbB-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 59.29% (G:12.14% B:0.44%) | 59.43% (G:12.05% B:0.44%) |
| Opponent Winning Chances: | 40.71% (G:9.00% B:0.34%) | 40.57% (G:9.21% B:0.36%) |
| Cubeless Equities | +0.218 | +0.436 |
| Cubeful Equities | ||
| No double: | +0.183 | ±0.006 (+0.177..+0.189) |
| Double/Take: | +0.135 (-0.048) | ±0.010 (+0.125..+0.145) |
| Double/Pass: | +1.000 (+0.817) | |
| Best Cube action: No double / Take | ||
| Percentage of wrong pass needed to make the double decision right: 5.2% | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 15529142 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 13 minutes 08 seconds | ||
eXtreme Gammon Version: 2.10
Naturally, with such a marginal double in the OP it's not a redouble.
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| XGID=-bBBBBCB-----------cccbbB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 60.90% (G:12.96% B:0.48%) | 61.44% (G:12.57% B:0.48%) |
| Opponent Winning Chances: | 39.10% (G:8.75% B:0.36%) | 38.56% (G:8.74% B:0.35%) |
| Cubeless Equities | +0.261 | +0.537 |
| Cubeful Equities | ||
| No redouble: | +0.404 | ±0.004 (+0.400..+0.408) |
| Redouble/Take: | +0.275 (-0.129) | ±0.009 (+0.266..+0.285) |
| Redouble/Pass: | +1.000 (+0.596) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 15.1% | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 15529142 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 19 minutes 54 seconds | ||
eXtreme Gammon Version: 2.10
If we have more pips to spare before breaking our full prime, white will find it difficult to take.
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| XGID=-bBBBBBB-----A-----cccbbB-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.19% (G:14.95% B:0.57%) | 73.32% (G:15.18% B:0.60%) |
| Opponent Winning Chances: | 26.81% (G:5.24% B:0.24%) | 26.68% (G:5.26% B:0.22%) |
| Cubeless Equities | +0.564 | +1.139 |
| Cubeful Equities | ||
| No double: | +0.663 (-0.287) | ±0.007 (+0.656..+0.670) |
| Double/Take: | +0.950 | ±0.009 (+0.941..+0.959) |
| Double/Pass: | +1.000 (+0.050) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 15529142 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 13 minutes 34 seconds | ||
eXtreme Gammon Version: 2.10
 |
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| XGID=-bBBBBBB------A----cccbbB-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 74.97% (G:15.73% B:0.63%) | 75.22% (G:15.75% B:0.68%) |
| Opponent Winning Chances: | 25.03% (G:4.69% B:0.21%) | 24.78% (G:4.70% B:0.20%) |
| Cubeless Equities | +0.614 | +1.239 |
| Cubeful Equities | ||
| No double: | +0.731 (-0.269) | ±0.006 (+0.725..+0.737) |
| Double/Take: | +1.064 (+0.064) | ±0.008 (+1.056..+1.072) |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 15529142 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 13 minutes 42 seconds | ||
eXtreme Gammon Version: 2.10
Finally, here is the position from Backgammon Boot Camp that Tim mentioned. Due to deeper white spares placement we don't really have bad non-jocker rolls that place our spares into worse spots than white's. It is a very strong double now
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| XGID=-bBBBBCB-----------bbcccB-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 69.99% (G:15.47% B:0.60%) | 70.13% (G:15.78% B:0.65%) |
| Opponent Winning Chances: | 30.01% (G:5.49% B:0.21%) | 29.87% (G:5.58% B:0.20%) |
| Cubeless Equities | +0.504 | +1.018 |
| Cubeful Equities | ||
| No double: | +0.564 (-0.241) | ±0.005 (+0.559..+0.569) |
| Double/Take: | +0.805 | ±0.009 (+0.796..+0.815) |
| Double/Pass: | +1.000 (+0.195) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 16811921 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 11 minutes 15 seconds | ||
eXtreme Gammon Version: 2.10
as well as a redouble
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| XGID=-bBBBBCB-----------bbcccB-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 69.65% (G:16.10% B:0.65%) | 70.13% (G:15.78% B:0.65%) |
| Opponent Winning Chances: | 30.35% (G:5.62% B:0.22%) | 29.87% (G:5.58% B:0.20%) |
| Cubeless Equities | +0.502 | +1.018 |
| Cubeful Equities | ||
| No redouble: | +0.676 (-0.129) | ±0.005 (+0.671..+0.681) |
| Redouble/Take: | +0.805 | ±0.009 (+0.796..+0.815) |
| Redouble/Pass: | +1.000 (+0.195) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 16811921 Moves: 4-ply, cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 18 minutes 42 seconds | ||
eXtreme Gammon Version: 2.10