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| XGID=---B-aD-C-B-dD---baeb-----:0:0:1:00:0:0:3:0:10 | |||||
Original: Blue leads by 9 pips. Cube action? | |||||
This is the original position, posted by Igor: #34 from Advanced Backgammon. (It can be reached by the sequence 65R-65R-21$-65R-52P-51D-61B-51H-55B-44P-C.) Blue on roll; cube action?
Igor has not posted a rollout for this position yet, however I can estimate the equity from other rollouts that have been done.
The diagrams below increase Blue's lead from 9 to 10 pips. Whether it is a pass or a take depends upon which extra pip White is given. For my variant in the left-hand diagram, White's take equity is 1.034 (she should pass). For NBM's variant in the right-hand diagram, White's equity is 0.979; owning the bar point gives her a small take. For the rollout details, see NBM's post.
The difference in take equity between the first two rollout results in Paul's post is .035, which I'll apply as the approximate adjustment for each pip in the race for this category of position. This suggests that if the two positions below somehow had 9-pip instead of 10-pip differences, the take equities would be 0.999 and 0.944.
If, for simplicity's sake, we say that the original position is, in character, roughly midway between that of variant 1 and variant 2, the take equity of the original position should be around 0.97. In other words, give or take .01, we can predict Blue's double/take equity to be 0.97 in Igor's rollout (not yet posted).
Scroll down to see rollouts for the two additional variants I later posted.
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| XGID=---B-aD-C-B-dD---c-eb-----:0:0:1:00:0:0:3:0:10 | |||||
Variant 1: Blue leads by 10 pips. Cube action? | |||||
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| XGID=---B-aD-C-B-dD---bbdb-----:0:0:1:00:0:0:3:0:10 | |||||
Variant 2: Blue leads by 10 pips. Cube action? | |||||
Variants 3 and 4 are instructive. In variant 3 (below, left -- if your window is wide enough), Blue should hit with 62, 52, 43 and 41, rolls that he should not hit with in any of the three positions above. White is down only 6 pips; however, due to her inflexible position, she is at a clear disadvantage tactically, and can squeeze out only a bare take (-0.988) against correctly aggressive play. [If the bot's play for Blue can be further improved upon, this just might be a theoretical pass.]
In variant 4 (below, right -- or further below), Blue is down 14 pips against White's extremely weak forward position and should play with wild abandon. He should hit with all rolls that he can, including 65, 61 and even 22. For the two rolls with which he cannot hit (64 and 42), he should start two points in front of White, to make it as difficult as possible to escape without hitting.
In the process of attacking, if a Blue checker -- or especially more than one blue checker -- is sent back, it seems unlikely to very unlikely that White can bring her position safely home. Hence, if White gives Blue credit for playing the position properly after doubling, she should pass. (It is a take equity of -1.009, according to the rollout).
Nack
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| XGID=---B-aD-C-B-bD-b-c-g------:0:0:1:00:0:0:3:0:10 | |||||
Variant 3: Blue leads by 6 pips. Cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.552% (G:12.236% B:0.192%) | 73.867% (G:13.581% B:0.273%) |
| Opponent Winning Chances: | 26.448% (G:2.538% B:0.076%) | 26.133% (G:2.687% B:0.105%) |
| Cubeless Equities | +0.5692 | +1.1759 |
| Cubeful Equities | ||
| No double: | +0.8109 (-0.1768) | ±0.0026 (+0.8083..+0.8135) |
| Double/Take: | +0.9877 | ±0.0044 (+0.9833..+0.9921) |
| Double/Pass: | +1.0000 (+0.0123) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 10368 Games rolled with Variance Reduction. Dice Seed: 29046005 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 2 hours 39 minutes | ||
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| XGID=---B-aD-C-B--D-b---l------:0:0:1:00:0:0:3:0:10 | |||||
Variant 4: Blue TRAILS by 14 pips. Cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 73.686% (G:11.158% B:0.384%) | 74.044% (G:14.647% B:0.736%) |
| Opponent Winning Chances: | 26.314% (G:3.490% B:0.104%) | 25.956% (G:3.361% B:0.127%) |
| Cubeless Equities | +0.5532 | +1.1997 |
| Cubeful Equities | ||
| No double: | +0.7947 (-0.2053) | ±0.0033 (+0.7914..+0.7980) |
| Double/Take: | +1.0091 (+0.0091) | ±0.0050 (+1.0041..+1.0141) |
| Double/Pass: | +1.0000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 23328 Games rolled with Variance Reduction. Dice Seed: 81920408 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 4 hours 53 minutes | ||