There isn't much left for me to discuss after Nack and Paul dissected the position. If this were a pure race white could take with no more than 14 pip deficit. The minimal contact left in the position favors blue. By how much? It depends on the strength of white's half of the board position. The weaker white's position the more aggressively blue can hit the white straggler. In the OP white has just enough for a thin take.
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| XGID=---B-aD-C-B-dD---baeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 74.02% (G:9.09% B:0.09%) | 74.27% (G:9.88% B:0.10%) |
| Opponent Winning Chances: | 25.98% (G:1.56% B:0.04%) | 25.73% (G:1.68% B:0.04%) |
| Cubeless Equities | +0.556 | +1.136 |
| Cubeful Equities | ||
| No double: | +0.832 (-0.129) | ±0.005 (+0.827..+0.837) |
| Double/Take: | +0.961 | ±0.007 (+0.954..+0.969) |
| Double/Pass: | +1.000 (+0.039) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Dice Seed: 86477631 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 7 minutes 34 seconds | ||
eXtreme Gammon Version: 2.10
Keep the same take point but reduce white's recube power and it becomes a drop.
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| XGID=---B-aD-C-B-dD---baeb-----:0:0:1:00:0:2:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.72% (G:10.43% B:0.10%) | 74.06% (G:10.62% B:0.10%) |
| Opponent Winning Chances: | 26.28% (G:1.90% B:0.06%) | 25.94% (G:1.88% B:0.07%) |
| Cubeless Equities | +0.561 | +1.173 |
| Cubeful Equities | ||
| No double: | +0.874 (-0.126) | ±0.006 (+0.868..+0.881) |
| Double/Take: | +1.046 (+0.046) | ±0.010 (+1.036..+1.056) |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 27547115 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 4 minutes 29 seconds | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
The other way around -- more recube power to white -- is a clear take.
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| XGID=---B-aD-C-B-dD---baeb-----:0:0:1:00:4:2:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 74.10% (G:9.92% B:0.13%) | 74.45% (G:9.86% B:0.36%) |
| Opponent Winning Chances: | 25.90% (G:1.70% B:0.04%) | 25.55% (G:1.76% B:0.04%) |
| Cubeless Equities | +0.583 | +1.255 |
| Cubeful Equities | ||
| No double: | +0.845 (-0.088) | ±0.008 (+0.837..+0.853) |
| Double/Take: | +0.933 | ±0.012 (+0.921..+0.945) |
| Double/Pass: | +1.000 (+0.067) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 27547115 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 6 minutes 39 seconds | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Adding just one more checker in the zone for blue is enough to force white to drop.
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| XGID=---B-aD-C-C-cC-a-baeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 75.46% (G:8.46% B:0.10%) | 75.78% (G:9.98% B:0.13%) |
| Opponent Winning Chances: | 24.54% (G:1.50% B:0.04%) | 24.22% (G:1.68% B:0.05%) |
| Cubeless Equities | +0.579 | +1.198 |
| Cubeful Equities | ||
| No double: | +0.870 (-0.130) | ±0.007 (+0.863..+0.877) |
| Double/Take: | +1.037 (+0.037) | ±0.011 (+1.025..+1.048) |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 62901579 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 3 minutes 08 seconds | ||
eXtreme Gammon Version: 2.10
As for the other variants, let's see what changes if we start moving white straggler one pip back at a time.
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| XGID=---Ba-D-C-B-dD---baeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 74.36% (G:10.84% B:0.11%) | 74.31% (G:12.12% B:0.12%) |
| Opponent Winning Chances: | 25.64% (G:2.26% B:0.06%) | 25.69% (G:2.44% B:0.08%) |
| Cubeless Equities | +0.573 | +1.167 |
| Cubeful Equities | ||
| No double: | +0.882 (-0.118) | ±0.001 (+0.881..+0.883) |
| Double/Take: | +1.001 (+0.001) | ±0.002 (+0.999..+1.003) |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 46656 Games rolled with Variance Reduction. Dice Seed: 86477631 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 88.6% | |
| Duration: 5 hours 19 minutes | ||
eXtreme Gammon Version: 2.10
By moving white straggler one pip back we effectively made race deficit one pip more and it is now a borderline decision. Restoring the race deficit back to 9 pips gives a clear take.
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| XGID=---Ba-D-C-B-dD---abeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.81% (G:10.25% B:0.09%) | 73.84% (G:11.50% B:0.10%) |
| Opponent Winning Chances: | 26.19% (G:2.24% B:0.06%) | 26.16% (G:2.42% B:0.07%) |
| Cubeless Equities | +0.557 | +1.136 |
| Cubeful Equities | ||
| No double: | +0.852 (-0.106) | ±0.008 (+0.843..+0.860) |
| Double/Take: | +0.958 | ±0.012 (+0.946..+0.969) |
| Double/Pass: | +1.000 (+0.042) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 27547115 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 4 minutes 15 seconds | ||
eXtreme Gammon Version: 2.10
Moving it further to 23 and 24 points still keeps white in the race take window, but allows a more flexible game plan -- stay back and harass blue or switch to a race if big numbers are rolled.
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| XGID=--aB--D-C-B-dD---baeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.76% (G:10.83% B:0.12%) | 74.18% (G:11.90% B:0.13%) |
| Opponent Winning Chances: | 26.24% (G:2.76% B:0.06%) | 25.82% (G:2.93% B:0.08%) |
| Cubeless Equities | +0.557 | +1.148 |
| Cubeful Equities | ||
| No double: | +0.876 (-0.099) | ±0.005 (+0.871..+0.881) |
| Double/Take: | +0.975 | ±0.008 (+0.966..+0.983) |
| Double/Pass: | +1.000 (+0.025) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Dice Seed: 45820022 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 7 minutes 40 seconds | ||
eXtreme Gammon Version: 2.10
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| XGID=-a-B--D-C-B-dD---baeb-----:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.26% (G:9.92% B:0.15%) | 73.47% (G:10.40% B:0.16%) |
| Opponent Winning Chances: | 26.74% (G:3.07% B:0.07%) | 26.53% (G:3.27% B:0.09%) |
| Cubeless Equities | +0.535 | +1.083 |
| Cubeful Equities | ||
| No double: | +0.852 (-0.052) | ±0.007 (+0.845..+0.859) |
| Double/Take: | +0.904 | ±0.011 (+0.893..+0.915) |
| Double/Pass: | +1.000 (+0.096) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 45820022 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 4 minutes 20 seconds | ||
eXtreme Gammon Version: 2.10