My comment about that first example was "There is probably a Wisecarver paradox position similar to this. Maybe give a checker or two back on the board."
It was a little harder to modify than I thought it would be but I found a likely similar example. It may be surprising how great the equity difference is between the best play which gets cubed and the second best play which does not. I had to push the made 2 point to the one point to make the single blot play fare relatively better and also put 9 checkers on the 3 point making opponent better after either play:
After 18/13, 4/1* it is a small cube and your equity is -.448. After 18/10 doubling is possibly a blunder but your equity of -.826 is lower by a huge amount.
In the original thread I asked where one might have seen the second position but no one responded. It is a misanalyzed problem from Robertie's 501.
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| XGID=aA-IAaa--a--aA-----bbbb-b-:1:-1:-1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 71.57% (G:0.00% B:0.00%) | 72.42% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 28.43% (G:14.27% B:0.26%) | 27.58% (G:14.32% B:0.26%) |
| Cubeless Equities | +0.286 | +0.605 |
| Cubeful Equities | ||
| No redouble: | +0.439 (-0.009) | ±0.003 (+0.435..+0.442) |
| Redouble/Take: | +0.448 | ±0.011 (+0.437..+0.459) |
| Redouble/Pass: | +1.000 (+0.552) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Moves and cube decisions: XG Roller+ | ||
| Double Decision confidence: | 94.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 5 hours 25 minutes | ||
eXtreme Gammon Version: 2.10
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| XGID=-a-IBaa--aA-a------bbbb-b-:1:-1:-1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 74.51% (G:0.00% B:0.00%) | 75.26% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 25.49% (G:7.41% B:0.36%) | 24.74% (G:7.67% B:0.42%) |
| Cubeless Equities | +0.413 | +0.849 |
| Cubeful Equities | ||
| No redouble: | +0.826 | ±0.019 (+0.807..+0.846) |
| Redouble/Take: | +0.719 (-0.108) | ±0.028 (+0.690..+0.747) |
| Redouble/Pass: | +1.000 (+0.174) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 27.7% | ||
| Rollout details | ||
| 165 Games rolled with Variance Reduction. Moves and cube decisions: XG Roller+ | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 27 minutes 36 seconds | ||
eXtreme Gammon Version: 2.10