–
The last six turns have been brutal for Blue. Back then, he had reasonable expectations of winning a gammon. Here is the position before all the fun began.
Including the upcoming roll, White will be on the bar for three of his next six turns. Each time, he will face a five-point board. Each time, he will enter on the first try. On four of the six turns, White will hit a Blue checker. Blue has been scrambling, hitting back whenever he can, but now he is down to his last gasp.
This is an easy choice. Not to hit means practically conceding the game, and throwing in an extra bunch of gammons as well. If Blue does not hit, then White can roll a 3 to complete his prime, while 5 and 6 escape his last checker. In case those options don’t attract him, White can hit with 2, 3, 5, 6, 7, 8 and 9. These hitting options are a large part of what gives White so many gammons. When Blue plays the “safe” 4/1, White wins 90% of the games, with a whopping 34% as gammons. If Blue hits instead, playing the banana split, he will lose a gammon 5% more often, but he will lift his winning percentage from 10% to 22%. According to the rollout, that’s a trade that is worth 0.2 points of equity. Either way, White is too good to double, way too good when Blue plays 4/1. Three rollouts follow. The first is for the original position. The others show White’s doubling decision after each of Blue’s candidate moves. Mike | ||||||||||||||||
Original Position
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| XGID=-BaCCBB--------b-babbcbAAA:1:-1:1:31:0:0:3:0:10 | |||||
| Blue to play 31 | |||||
| 1. | Rollout1 | Bar/24 5/2* | eq: -1.0526 | |||
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| 2. | Rollout1 | Bar/24 4/1 | eq: -1.2541 (-0.2015) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 70867082 Moves: 3-ply, cube decisions: XG Roller | ||||||
eXtreme Gammon Version: 2.03
Cube Action after Bar/24, 5/2*
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| XGID=aBACCAB--------b-babbcbAB-:1:-1:-1:00:0:0:3:0:10 | |||||
| White on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 77.208% (G:38.676% B:4.933%) | 77.389% (G:38.173% B:4.880%) |
| Opponent Winning Chances: | 22.792% (G:6.882% B:0.077%) | 22.611% (G:6.816% B:0.079%) |
| Cubeless Equities | +0.9107 | +1.8187 |
| Cubeful Equities | ||
| No redouble: | +1.0524 | ±0.0052 (+1.0472..+1.0577) |
| Redouble/Take: | +1.6588 (+0.6064) | ±0.0084 (+1.6504..+1.6672) |
| Redouble/Pass: | +1.0000 (-0.0524) | |
| Best Cube action: Too good to redouble / Pass | ||
| Percentage of wrong take needed to make the double decision right: 8.0% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 46307534 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 17 minutes 30 seconds | ||
eXtreme Gammon Version: 2.03
Cube Action after Bar/24, 4/1
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| XGID=-CaCBBB--------b-babbcbAB-:1:-1:-1:00:0:0:3:0:10 | |||||
| White on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 90.348% (G:33.807% B:2.362%) | 90.723% (G:33.454% B:2.386%) |
| Opponent Winning Chances: | 9.652% (G:0.972% B:0.015%) | 9.277% (G:0.908% B:0.013%) |
| Cubeless Equities | +1.1588 | +2.3273 |
| Cubeful Equities | ||
| No redouble: | +1.2517 | ±0.0025 (+1.2492..+1.2542) |
| Redouble/Take: | +2.2605 (+1.0088) | ±0.0052 (+2.2553..+2.2658) |
| Redouble/Pass: | +1.0000 (-0.2517) | |
| Best Cube action: Too good to redouble / Pass | ||
| Percentage of wrong take needed to make the double decision right: 20.0% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 9879925 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 18 minutes 34 seconds | ||
eXtreme Gammon Version: 2.03