It's clear that the question is whether we are too good or not. Here is my attempt to put some numbers together. I'll just throw in all relevant facts that come to mind.
1. If we manage to escape our checker and hence close one white checker out how many gammons do we win? According to one of Phil Simborg's USBGF videos there is a rule of thumb due to David Rockwell that goes as follows (I'm citing this from memory, so I don't guarantee that all this is 100% correct): For the first 8 pips that white checkers in the outfield need to get to her inner board, she loses 10% gammon. For each next 4 pips, add extra 10% gammon losses. In our position white has 16 pips to get home, so it's about 30% gammon wins for us in this case.
2. It takes just slightly over 3 rolls on average to roll a given number, such as 6. (Again, I did a quick calculation myself and don't guarantee that it's 100% correct.)
3. We have 18 pips to spare before we would have to start breaking our home board; this is just about 2 rolls.
4. The probability of us rolling a 6 within the next 3 rolls is about 2/3.
It looks like we escape our checker before starting to break our home board about 2/3 of the time. This gives us 2/9 gammons and 4/9 single wins.
What happens in the remaining 3/9 games where we fail to escape before having to break our board? Does white win at least 2/9 among those? Even if we break our board we can still win, so this is getting too complicated for me.
I failed to provide a reasonable calculation, so I'll just post the rollout results. It turns out that 18-20 pips are not enough to continue, while 21 pips of "reserve" allows us to play on. The decisions are very close, so you won't be too far off by making either choice.
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| XGID=aBBBBBC-----b-A---bcbcbA--:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 76.16% (G:26.35% B:0.04%) | 76.80% (G:25.91% B:0.03%) |
| Opponent Winning Chances: | 23.84% (G:1.91% B:0.05%) | 23.20% (G:1.86% B:0.04%) |
| Cubeless Equities | +0.768 | +1.553 |
| Cubeful Equities | ||
| No redouble: | +0.980 (-0.020) | ±0.006 (+0.975..+0.986) |
| Redouble/Take: | +1.365 (+0.365) | ±0.009 (+1.356..+1.374) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 4871902 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 minute 01 second | ||
eXtreme Gammon Version: 2.10
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| XGID=aBBBBBC-----b--A--bcbcbA--:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 76.56% (G:26.73% B:0.04%) | 77.23% (G:26.35% B:0.04%) |
| Opponent Winning Chances: | 23.44% (G:2.08% B:0.06%) | 22.77% (G:2.08% B:0.06%) |
| Cubeless Equities | +0.778 | +1.574 |
| Cubeful Equities | ||
| No redouble: | +0.996 (-0.004) | ±0.001 (+0.994..+0.997) |
| Redouble/Take: | +1.382 (+0.382) | ±0.002 (+1.380..+1.385) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 20736 Games rolled with Variance Reduction. Dice Seed: 4871902 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 11 minutes 54 seconds | ||
eXtreme Gammon Version: 2.10
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| XGID=aBBBBBC-----b---A-bcbcbA--:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 76.86% (G:27.06% B:0.04%) | 77.58% (G:26.66% B:0.05%) |
| Opponent Winning Chances: | 23.14% (G:2.42% B:0.09%) | 22.42% (G:2.38% B:0.09%) |
| Cubeless Equities | +0.783 | +1.588 |
| Cubeful Equities | ||
| No redouble: | +0.989 (-0.011) | ±0.003 (+0.986..+0.992) |
| Redouble/Take: | +1.416 (+0.416) | ±0.006 (+1.410..+1.421) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Dice Seed: 4871902 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 minute 17 seconds | ||
eXtreme Gammon Version: 2.10
In the two variants above notice how badly 44 plays in the second position, while how not so badly 55 plays in the first position.
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| XGID=aBBBBBC-----b----AbcbcbA--:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 78.72% (G:27.67% B:0.04%) | 79.54% (G:27.17% B:0.04%) |
| Opponent Winning Chances: | 21.28% (G:1.75% B:0.05%) | 20.46% (G:1.73% B:0.05%) |
| Cubeless Equities | +0.834 | +1.690 |
| Cubeful Equities | ||
| No redouble: | +1.033 | ±0.003 (+1.030..+1.036) |
| Redouble/Take: | +1.530 (+0.497) | ±0.007 (+1.523..+1.538) |
| Redouble/Pass: | +1.000 (-0.033) | |
| Best Cube action: Too good to redouble / Pass | ||
| Percentage of wrong take needed to make the double decision right: 6.2% | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 4871902 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 33.6 seconds | ||
eXtreme Gammon Version: 2.10