You can read the original rec.games.backgammon thread on Google Groups. I posted the rollout below, with the following comments: "O's timing might not look that bad, but one needs a lot of timing to play a 12-backgame. O's main hope here is for X to roll big right away. XG says that if X rolls something like 51, then he loses his market. Given that, it makes sense to double now."
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| XGID=-bbBBBFB-A--a-a--a-bbbb---:0:0:1:00:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 64.91% (G:30.82% B:4.12%) | 64.69% (G:30.49% B:4.23%) |
| Opponent Winning Chances: | 35.09% (G:1.52% B:0.05%) | 35.31% (G:1.54% B:0.06%) |
| Cubeless Equities | +0.632 | +1.250 |
| Cubeful Equities | ||
| No double: | +0.836 (-0.105) | ±0.011 (+0.825..+0.847) |
| Double/Take: | +0.941 | ±0.021 (+0.920..+0.961) |
| Double/Pass: | +1.000 (+0.059) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 4 minutes 09 seconds | ||
eXtreme Gammon Version: 2.19.211.pre-release
After I posted the above rollout, Stick remarked, "This is a much bigger take than 3 ply/XGR would suggest." Stick often regards a 0.020 equity difference as big, so that's what I assumed he meant here. Sure enough, my XGR+ rollout below indicates a bigger take (though of course there's still some variance in both rollouts).
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| XGID=-bbBBBFB-A--a-a--a-bbbb---:0:0:1:00:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 64.71% (G:30.74% B:4.11%) | 64.46% (G:30.48% B:4.11%) |
| Opponent Winning Chances: | 35.29% (G:1.59% B:0.06%) | 35.54% (G:1.61% B:0.06%) |
| Cubeless Equities | +0.626 | +1.237 |
| Cubeful Equities | ||
| No double: | +0.841 (-0.079) | ±0.006 (+0.835..+0.846) |
| Double/Take: | +0.920 | ±0.011 (+0.909..+0.931) |
| Double/Pass: | +1.000 (+0.080) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 2592 Games rolled with Variance Reduction. Dice Seed: 271828 Moves and cube decisions: XG Roller+ Search interval: Large | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 8 hours 29 minutes | ||
eXtreme Gammon Version: 2.19.211.pre-release
Stick followed up by saying, "Sorry but my own rollout which is ++/++ gigantic has this being worth +0.890." Intrigued, I did my own XGR++ Gigantic rollout, but was not able to corroborate Stick's result. Perhaps Stick can post his rollout here so that we can compare results. It would be pretty interesting to me to see such a big difference between two separate XGR++ Gigantic rollouts.
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| XGID=-bbBBBFB-A--a-a--a-bbbb---:0:0:1:00:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 64.85% (G:30.85% B:4.07%) | 64.47% (G:30.61% B:4.10%) |
| Opponent Winning Chances: | 35.15% (G:1.52% B:0.05%) | 35.53% (G:1.61% B:0.06%) |
| Cubeless Equities | +0.630 | +1.240 |
| Cubeful Equities | ||
| No double: | +0.840 (-0.086) | ±0.009 (+0.831..+0.848) |
| Double/Take: | +0.925 | ±0.015 (+0.911..+0.940) |
| Double/Pass: | +1.000 (+0.075) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves and cube decisions: XG Roller++ Search interval: Gigantic | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 2 days 10 hours 23 minutes | ||
eXtreme Gammon Version: 2.19.211.pre-release