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501 Essential Backgammon Problems #104  Rollout + Variants
Posted By: Igor
Date: Thursday, 3 October 2013, at 2:27 p.m.
In Response To: 501 Essential Backgammon Problems #104 (Igor)
Robertie discards 24/21 since when you are behind in the race you should not break contact. But how are you going to win this game? White's position is flexible enough to hardly leave any shots. Our best shot is to step up and then hop out with any 6. Any move not containing 24/21 is a big error.
White is Player 2
score: 0
pip: 125Unlimited Game
Jacobypip: 138
score: 0
Blue is Player 1XGID=BDBBAcCbcbeA:0:0:1:33:0:0:1:0:10 Blue to play 33
1. Rollout^{1} 24/21 11/5 8/5 eq: 0.624
Player:
Opponent:32.38% (G:2.33% B:0.06%)
67.62% (G:5.97% B:0.10%)Conf.: ± 0.001 (0.625...0.622)  [50.6%]
Duration: 1 hour 44 minutes2. Rollout^{1} 24/21 13/10 8/5(2) eq: 0.624 (0.000)
Player:
Opponent:32.42% (G:2.28% B:0.05%)
67.58% (G:5.84% B:0.11%)Conf.: ± 0.001 (0.625...0.622)  [49.4%]
Duration: 1 hour 39 minutes3. Rollout^{2} 24/21 9/6 8/5(2) eq: 0.634 (0.010)
Player:
Opponent:31.94% (G:2.23% B:0.05%)
68.06% (G:6.14% B:0.12%)Conf.: ± 0.003 (0.637...0.631)  [0.0%]
Duration: 22 minutes 40 seconds4. Rollout^{2} 24/21 13/7 11/8 eq: 0.642 (0.019)
Player:
Opponent:31.27% (G:2.19% B:0.07%)
68.73% (G:7.75% B:0.17%)Conf.: ± 0.004 (0.647...0.638)  [0.0%]
Duration: 17 minutes 47 seconds5. Rollout^{3} 24/21 8/5(2) 6/3 eq: 0.649 (0.025)
Player:
Opponent:31.75% (G:2.21% B:0.05%)
68.25% (G:6.81% B:0.12%)Conf.: ± 0.004 (0.654...0.645)  [0.0%]
Duration: 12 minutes 40 seconds6. Rollout^{3} 24/21 13/10 11/5 eq: 0.649 (0.026)
Player:
Opponent:31.71% (G:2.19% B:0.05%)
68.29% (G:6.40% B:0.14%)Conf.: ± 0.005 (0.654...0.645)  [0.0%]
Duration: 12 minutes 05 seconds7. Rollout^{3} 24/21 13/4 eq: 0.656 (0.032)
Player:
Opponent:31.54% (G:2.20% B:0.05%)
68.46% (G:6.81% B:0.16%)Conf.: ± 0.005 (0.661...0.651)  [0.0%]
Duration: 11 minutes 29 seconds8. Rollout^{3} 24/21 13/10 11/8 9/6 eq: 0.663 (0.039)
Player:
Opponent:30.82% (G:2.61% B:0.08%)
69.18% (G:8.09% B:0.20%)Conf.: ± 0.007 (0.670...0.656)  [0.0%]
Duration: 8 minutes 55 seconds9. Rollout^{4} 24/21 11/5 9/6 eq: 0.669 (0.045)
Player:
Opponent:31.19% (G:2.35% B:0.06%)
68.81% (G:7.16% B:0.18%)Conf.: ± 0.006 (0.675...0.662)  [0.0%]
Duration: 5 minutes 37 seconds10. Rollout^{4} 24/21 11/5 6/3 eq: 0.669 (0.045)
Player:
Opponent:30.85% (G:2.31% B:0.08%)
69.15% (G:8.39% B:0.16%)Conf.: ± 0.008 (0.677...0.661)  [0.0%]
Duration: 4 minutes 37 seconds11. Rollout^{3} 24/21 13/7 9/6 eq: 0.670 (0.046)
Player:
Opponent:30.75% (G:2.39% B:0.07%)
69.25% (G:7.91% B:0.23%)Conf.: ± 0.006 (0.676...0.664)  [0.0%]
Duration: 8 minutes 34 seconds12. Rollout^{3} 24/21 13/7 8/5 eq: 0.670 (0.047)
Player:
Opponent:31.20% (G:2.45% B:0.06%)
68.80% (G:7.75% B:0.28%)Conf.: ± 0.005 (0.675...0.666)  [0.0%]
Duration: 12 minutes 11 seconds13. Rollout^{3} 13/10 11/5 8/5 eq: 0.672 (0.048)
Player:
Opponent:31.20% (G:3.44% B:0.06%)
68.80% (G:5.94% B:0.13%)Conf.: ± 0.005 (0.677...0.667)  [0.0%]
Duration: 13 minutes 58 seconds14. Rollout^{3} 24/21 13/10 11/8 6/3 eq: 0.679 (0.055)
Player:
Opponent:30.72% (G:2.21% B:0.06%)
69.28% (G:8.52% B:0.18%)Conf.: ± 0.006 (0.685...0.673)  [0.0%]
Duration: 8 minutes 59 seconds15. Rollout^{3} 11/5 8/5(2) eq: 0.682 (0.058)
Player:
Opponent:31.00% (G:3.32% B:0.06%)
69.00% (G:6.02% B:0.12%)Conf.: ± 0.005 (0.687...0.677)  [0.0%]
Duration: 12 minutes 33 seconds^{1} 46656 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3ply, cube decisions: XG Roller
^{2} 10368 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3ply, cube decisions: XG Roller
^{3} 5184 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3ply, cube decisions: XG Roller
^{4} 2592 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3ply, cube decisions: XG RollereXtreme Gammon Version: 2.10
Close race does matter here. If we are just slightly more behind in the race, then we are better off staying back.
White is Player 2
score: 0
pip: 125Unlimited Game
Jacobypip: 143
score: 0
Blue is Player 1XGID=BCBBBcCbcbeA:0:0:1:33:0:0:1:0:10 Blue to play 33
1. Rollout^{1} 13/10 11/5 8/5 eq: 0.774
Player:
Opponent:28.08% (G:3.21% B:0.07%)
71.92% (G:7.11% B:0.14%)Conf.: ± 0.006 (0.780...0.768)  [77.1%]
Duration: 10 minutes 00 second2. Rollout^{1} 11/5(2) eq: 0.777 (0.003)
Player:
Opponent:28.48% (G:3.12% B:0.07%)
71.52% (G:6.99% B:0.11%)Conf.: ± 0.005 (0.781...0.772)  [22.9%]
Duration: 12 minutes 09 seconds3. Rollout^{1} 11/5 8/5(2) eq: 0.792 (0.018)
Player:
Opponent:27.70% (G:3.12% B:0.07%)
72.30% (G:7.13% B:0.12%)Conf.: ± 0.006 (0.798...0.786)  [0.0%]
Duration: 8 minutes 43 seconds4. Rollout^{1} 13/7 8/5(2) eq: 0.795 (0.021)
Player:
Opponent:27.69% (G:3.03% B:0.07%)
72.31% (G:7.07% B:0.14%)Conf.: ± 0.006 (0.801...0.788)  [0.0%]
Duration: 7 minutes 49 seconds5. Rollout^{1} 24/21 13/10 8/5(2) eq: 0.796 (0.022)
Player:
Opponent:28.04% (G:1.73% B:0.04%)
71.96% (G:7.03% B:0.10%)Conf.: ± 0.006 (0.802...0.790)  [0.0%]
Duration: 9 minutes 50 seconds6. Rollout^{1} 11/5 9/6 8/5 eq: 0.797 (0.023)
Player:
Opponent:27.64% (G:3.23% B:0.07%)
72.36% (G:7.27% B:0.14%)Conf.: ± 0.006 (0.803...0.791)  [0.0%]
Duration: 8 minutes 02 seconds7. Rollout^{1} 24/21 11/5 8/5 eq: 0.797 (0.023)
Player:
Opponent:28.05% (G:1.75% B:0.05%)
71.95% (G:7.11% B:0.11%)Conf.: ± 0.006 (0.803...0.791)  [0.0%]
Duration: 9 minutes 00 second8. Rollout^{1} 13/10 9/6 8/5(2) eq: 0.797 (0.023)
Player:
Opponent:27.59% (G:3.22% B:0.07%)
72.41% (G:7.16% B:0.16%)Conf.: ± 0.006 (0.803...0.791)  [0.0%]
Duration: 7 minutes 28 seconds^{1} 5184 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG RollereXtreme Gammon Version: 2.10
It really is a very fine line.
White is Player 2
score: 0
pip: 125Unlimited Game
Jacobypip: 142
score: 0
Blue is Player 1XGID=BCBBAAcCbcbeA:0:0:1:33:0:0:1:0:10 Blue to play 33
1. Rollout^{1} 24/21 13/10 8/5(2) eq: 0.745
Player:
Opponent:28.94% (G:1.81% B:0.05%)
71.06% (G:6.63% B:0.10%)Conf.: ± 0.002 (0.747...0.743)  [100.0%]
Duration: 1 hour 23 minutes2. Rollout^{1} 24/21 11/5 8/5 eq: 0.750 (0.005)
Player:
Opponent:28.88% (G:1.86% B:0.05%)
71.12% (G:6.83% B:0.10%)Conf.: ± 0.002 (0.751...0.748)  [0.0%]
Duration: 1 hour 19 minutes3. Rollout^{1} 13/10 9/6 8/5(2) eq: 0.750 (0.005)
Player:
Opponent:28.44% (G:3.23% B:0.07%)
71.56% (G:6.76% B:0.13%)Conf.: ± 0.002 (0.752...0.748)  [0.0%]
Duration: 1 hour 23 minutes4. Rollout^{2} 24/21 10/7 8/5(2) eq: 0.755 (0.010)
Player:
Opponent:28.80% (G:1.84% B:0.05%)
71.20% (G:6.87% B:0.10%)Conf.: ± 0.004 (0.759...0.751)  [0.0%]
Duration: 17 minutes 36 seconds5. Rollout^{3} 13/10 11/5 8/5 eq: 0.759 (0.014)
Player:
Opponent:29.05% (G:3.13% B:0.06%)
70.95% (G:6.57% B:0.11%)Conf.: ± 0.007 (0.765...0.752)  [0.0%]
Duration: 6 minutes 40 seconds6. Rollout^{3} 10/4 8/5(2) eq: 0.759 (0.014)
Player:
Opponent:28.96% (G:3.13% B:0.07%)
71.04% (G:6.47% B:0.11%)Conf.: ± 0.006 (0.765...0.753)  [0.0%]
Duration: 6 minutes 42 seconds7. Rollout^{3} 24/21 9/6 8/5(2) eq: 0.762 (0.017)
Player:
Opponent:28.63% (G:2.15% B:0.06%)
71.37% (G:7.17% B:0.12%)Conf.: ± 0.008 (0.769...0.754)  [0.0%]
Duration: 4 minutes 23 seconds^{1} 46656 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG Roller
^{2} 10368 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG Roller
^{3} 2592 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG RollereXtreme Gammon Version: 2.10
A couple more pips further behind in the race and it is stepping up that is a big error.
White is Player 2
score: 0
pip: 125Unlimited Game
Jacobypip: 145
score: 0
Blue is Player 1XGID=BCBBAcDbcbeA:0:0:1:33:0:0:1:0:10 Blue to play 33
1. Rollout^{1} 13/10(2) 8/5(2) eq: 0.837
Player:
Opponent:26.95% (G:2.99% B:0.07%)
73.05% (G:7.46% B:0.13%)Conf.: ± 0.004 (0.841...0.833)  [100.0%]
Duration: 29 minutes 01 second2. Rollout^{1} 13/10 11/5 8/5 eq: 0.846 (0.009)
Player:
Opponent:26.80% (G:3.10% B:0.07%)
73.20% (G:7.58% B:0.11%)Conf.: ± 0.004 (0.850...0.842)  [0.0%]
Duration: 27 minutes 46 seconds3. Rollout^{2} 13/10(2) 11/5 eq: 0.859 (0.022)
Player:
Opponent:26.70% (G:3.10% B:0.09%)
73.30% (G:8.25% B:0.14%)Conf.: ± 0.008 (0.867...0.851)  [0.0%]
Duration: 4 minutes 26 seconds4. Rollout^{2} 13/10 9/6 8/5(2) eq: 0.862 (0.025)
Player:
Opponent:26.37% (G:3.09% B:0.08%)
73.63% (G:7.57% B:0.14%)Conf.: ± 0.008 (0.870...0.854)  [0.0%]
Duration: 4 minutes 22 seconds5. Rollout^{2} 11/5 8/5(2) eq: 0.863 (0.026)
Player:
Opponent:26.46% (G:2.95% B:0.07%)
73.54% (G:7.71% B:0.11%)Conf.: ± 0.008 (0.871...0.855)  [0.0%]
Duration: 3 minutes 45 seconds6. Rollout^{2} 13/7 8/5(2) eq: 0.863 (0.026)
Player:
Opponent:26.50% (G:2.92% B:0.07%)
73.50% (G:7.56% B:0.12%)Conf.: ± 0.008 (0.871...0.855)  [0.0%]
Duration: 4 minutes 25 seconds7. Rollout^{2} 13/7(2) eq: 0.874 (0.037)
Player:
Opponent:26.50% (G:2.94% B:0.07%)
73.50% (G:8.37% B:0.13%)Conf.: ± 0.009 (0.883...0.865)  [0.0%]
Duration: 4 minutes 13 seconds8. Rollout^{2} 11/5 9/6 8/5 eq: 0.875 (0.038)
Player:
Opponent:26.21% (G:3.12% B:0.08%)
73.79% (G:7.94% B:0.12%)Conf.: ± 0.009 (0.884...0.867)  [0.0%]
Duration: 3 minutes 08 seconds9. Rollout^{2} 13/10 13/4 eq: 0.889 (0.051)
Player:
Opponent:26.46% (G:3.15% B:0.09%)
73.54% (G:9.09% B:0.23%)Conf.: ± 0.009 (0.897...0.880)  [0.0%]
Duration: 3 minutes 24 seconds10. Rollout^{2} 24/21 13/10 8/5(2) eq: 0.890 (0.053)
Player:
Opponent:26.32% (G:1.67% B:0.05%)
73.68% (G:7.78% B:0.10%)Conf.: ± 0.008 (0.898...0.881)  [0.0%]
Duration: 5 minutes 00 second11. Rollout^{2} 24/21 11/5 8/5 eq: 0.893 (0.056)
Player:
Opponent:26.31% (G:1.66% B:0.05%)
73.69% (G:7.95% B:0.09%)Conf.: ± 0.008 (0.901...0.885)  [0.0%]
Duration: 4 minutes 43 seconds^{1} 15552 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG Roller
^{2} 2592 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3ply, cube decisions: XG RollereXtreme Gammon Version: 2.10
Improving white distribution raises relative equity of stepping up.
White is Player 2
score: 0
pip: 126Unlimited Game
Jacobypip: 146
score: 0
Blue is Player 1XGID=BCBAAAcDbccdA:0:0:1:33:0:0:1:0:10 Blue to play 33
1. Rollout^{1} 13/10 11/5 8/5 eq: 0.972
Player:
Opponent:24.56% (G:2.52% B:0.07%)
75.44% (G:7.96% B:0.12%)Conf.: ± 0.003 (0.975...0.969)  [90.6%]
Duration: 29 minutes 37 seconds2. Rollout^{1} 10/4 8/5(2) eq: 0.975 (0.003)
Player:
Opponent:24.56% (G:2.63% B:0.06%)
75.44% (G:8.15% B:0.13%)Conf.: ± 0.003 (0.979...0.972)  [9.4%]
Duration: 28 minutes 34 seconds3. Rollout^{1} 13/7 8/5(2) eq: 0.982 (0.010)
Player:
Opponent:24.52% (G:2.54% B:0.06%)
75.48% (G:8.33% B:0.14%)Conf.: ± 0.004 (0.986...0.979)  [0.0%]
Duration: 25 minutes 18 seconds4. Rollout^{1} 24/21 13/10 8/5(2) eq: 0.985 (0.013)
Player:
Opponent:24.72% (G:1.58% B:0.05%)
75.28% (G:8.61% B:0.11%)Conf.: ± 0.003 (0.988...0.981)  [0.0%]
Duration: 31 minutes 05 seconds^{1} 15552 Games rolled with Variance Reduction.
Dice Seed: 40238487
Moves: 3ply, cube decisions: XG RollereXtreme Gammon Version: 2.10

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