Position is innocent looking rather than simple. Rick has given an excellent explanation to why the things the way they are. He was also able to estimate 7% difference which was later confirmed by rollouts.If you haven't read his post I strongly recommend you do so. Also, Rambiz got intuitively very close. I think nearly everyone understands that giving a dead cube has an effect, but i doubt I would have to take my shoes off to count those who understand how big that effect is.
Bellow you will find 3 rollouts. 1st one is ATS, where the redouble is marginally correct. 2nd is for money, where its a blunder to redouble. Finally, the 3rd one is also for money, but with cube cap at 8, where redouble is even slightly easier than ATS.
I believe this is an idea with quite a few interesting applications. Those who play for money with a cube limit set to a finite number should read Rick's comments. If you don't you're likely throwing your money away. More on that later in another post at another time. Stay tuned. ATS
                  |
| ||||
| XGID=-I-----------------b-abb--:2:1:1:00:0:0:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 63.76% (G:0.00% B:0.00%) | 63.76% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 36.24% (G:0.00% B:0.00%) | 36.24% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.275 | +0.524 |
| Cubeful Equities | ||
| No redouble: | +0.504 (-0.020) | ±0.001 (+0.503..+0.505) |
| Redouble/Take: | +0.524 | ±0.000 (+0.524..+0.524) |
| Redouble/Pass: | +1.000 (+0.476) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.2 second | ||
eXtreme Gammon Version: 2.02, MET: Rockwell-Kazaross
For Money
|
| ||||
| XGID=-I-----------------b-abb--:2:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 63.76% (G:0.00% B:0.00%) | 63.76% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 36.24% (G:0.00% B:0.00%) | 36.24% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.275 | +0.550 |
| Cubeful Equities | ||
| No redouble: | +0.462 | ±0.002 (+0.461..+0.464) |
| Redouble/Take: | +0.335 (-0.127) | ±0.002 (+0.332..+0.337) |
| Redouble/Pass: | +1.000 (+0.538) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 16.1% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.2 second | ||
eXtreme Gammon Version: 2.02
For Money Cube MAX 8
|
| ||||
| XGID=-I-----------------b-abb--:2:1:1:00:0:0:3:0:3 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 63.76% (G:0.00% B:0.00%) | 63.76% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 36.24% (G:0.00% B:0.00%) | 36.24% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.275 | +0.550 |
| Cubeful Equities | ||
| No redouble: | +0.521 (-0.030) | ±0.001 (+0.520..+0.521) |
| Redouble/Take: | +0.550 | ±0.000 (+0.550..+0.550) |
| Redouble/Pass: | +1.000 (+0.450) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.2 second | ||
eXtreme Gammon Version: 2.02