501 Essential Backgammon Problems #104 -- Rollout + Variants

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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: 125

Unlimited Game
Jacoby

pip: 138
score: 0

Blue is Player 1

XGID=---B--D-BB-AcC--bcbe----A-:0:0:1:33:0:0:1:0:10
Blue to play 33

1. Rollout¹ 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.: ą 0.001 (-0.625...-0.622) - [50.6%]
Duration: 1 hour 44 minutes
2. Rollout¹ 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.: ą 0.001 (-0.625...-0.622) - [49.4%]
Duration: 1 hour 39 minutes
3. Rollout² 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.: ą 0.003 (-0.637...-0.631) - [0.0%]
Duration: 22 minutes 40 seconds
4. Rollout² 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.: ą 0.004 (-0.647...-0.638) - [0.0%]
Duration: 17 minutes 47 seconds
5. Rollout³ 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.: ą 0.004 (-0.654...-0.645) - [0.0%]
Duration: 12 minutes 40 seconds
6. Rollout³ 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.: ą 0.005 (-0.654...-0.645) - [0.0%]
Duration: 12 minutes 05 seconds
7. Rollout³ 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.: ą 0.005 (-0.661...-0.651) - [0.0%]
Duration: 11 minutes 29 seconds
8. Rollout³ 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.: ą 0.007 (-0.670...-0.656) - [0.0%]
Duration: 8 minutes 55 seconds
9. Rollout⁴ 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.: ą 0.006 (-0.675...-0.662) - [0.0%]
Duration: 5 minutes 37 seconds
10. Rollout⁴ 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.: ą 0.008 (-0.677...-0.661) - [0.0%]
Duration: 4 minutes 37 seconds
11. Rollout³ 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.: ą 0.006 (-0.676...-0.664) - [0.0%]
Duration: 8 minutes 34 seconds
12. Rollout³ 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.: ą 0.005 (-0.675...-0.666) - [0.0%]
Duration: 12 minutes 11 seconds
13. Rollout³ 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.: ą 0.005 (-0.677...-0.667) - [0.0%]
Duration: 13 minutes 58 seconds
14. Rollout³ 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.: ą 0.006 (-0.685...-0.673) - [0.0%]
Duration: 8 minutes 59 seconds
15. Rollout³ 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.: ą 0.005 (-0.687...-0.677) - [0.0%]
Duration: 12 minutes 33 seconds

¹ 46656 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

² 10368 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

³ 5184 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

⁴ 2592 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

eXtreme 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: 125

Unlimited Game
Jacoby

pip: 143
score: 0

Blue is Player 1

XGID=---B--C-BB-BcC--bcbe----A-:0:0:1:33:0:0:1:0:10
Blue to play 33

1. Rollout¹ 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.: ą 0.006 (-0.780...-0.768) - [77.1%]
Duration: 10 minutes 00 second
2. Rollout¹ 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.: ą 0.005 (-0.781...-0.772) - [22.9%]
Duration: 12 minutes 09 seconds
3. Rollout¹ 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.: ą 0.006 (-0.798...-0.786) - [0.0%]
Duration: 8 minutes 43 seconds
4. Rollout¹ 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.: ą 0.006 (-0.801...-0.788) - [0.0%]
Duration: 7 minutes 49 seconds
5. Rollout¹ 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.: ą 0.006 (-0.802...-0.790) - [0.0%]
Duration: 9 minutes 50 seconds
6. Rollout¹ 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.: ą 0.006 (-0.803...-0.791) - [0.0%]
Duration: 8 minutes 02 seconds
7. Rollout¹ 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.: ą 0.006 (-0.803...-0.791) - [0.0%]
Duration: 9 minutes 00 second
8. Rollout¹ 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.: ą 0.006 (-0.803...-0.791) - [0.0%]
Duration: 7 minutes 28 seconds

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

It really is a very fine line.

White is Player 2

score: 0
pip: 125

Unlimited Game
Jacoby

pip: 142
score: 0

Blue is Player 1

XGID=---B--C-BBAAcC--bcbe----A-:0:0:1:33:0:0:1:0:10
Blue to play 33

1. Rollout¹ 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.: ą 0.002 (-0.747...-0.743) - [100.0%]
Duration: 1 hour 23 minutes
2. Rollout¹ 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.: ą 0.002 (-0.751...-0.748) - [0.0%]
Duration: 1 hour 19 minutes
3. Rollout¹ 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.: ą 0.002 (-0.752...-0.748) - [0.0%]
Duration: 1 hour 23 minutes
4. Rollout² 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.: ą 0.004 (-0.759...-0.751) - [0.0%]
Duration: 17 minutes 36 seconds
5. Rollout³ 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.: ą 0.007 (-0.765...-0.752) - [0.0%]
Duration: 6 minutes 40 seconds
6. Rollout³ 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.: ą 0.006 (-0.765...-0.753) - [0.0%]
Duration: 6 minutes 42 seconds
7. Rollout³ 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.: ą 0.008 (-0.769...-0.754) - [0.0%]
Duration: 4 minutes 23 seconds

¹ 46656 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

² 10368 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

³ 2592 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

eXtreme 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: 125

Unlimited Game
Jacoby

pip: 145
score: 0

Blue is Player 1

XGID=---B--C-BB-AcD--bcbe----A-:0:0:1:33:0:0:1:0:10
Blue to play 33

1. Rollout¹ 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.: ą 0.004 (-0.841...-0.833) - [100.0%]
Duration: 29 minutes 01 second
2. Rollout¹ 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.: ą 0.004 (-0.850...-0.842) - [0.0%]
Duration: 27 minutes 46 seconds
3. Rollout² 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.: ą 0.008 (-0.867...-0.851) - [0.0%]
Duration: 4 minutes 26 seconds
4. Rollout² 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.: ą 0.008 (-0.870...-0.854) - [0.0%]
Duration: 4 minutes 22 seconds
5. Rollout² 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.: ą 0.008 (-0.871...-0.855) - [0.0%]
Duration: 3 minutes 45 seconds
6. Rollout² 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.: ą 0.008 (-0.871...-0.855) - [0.0%]
Duration: 4 minutes 25 seconds
7. Rollout² 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.: ą 0.009 (-0.883...-0.865) - [0.0%]
Duration: 4 minutes 13 seconds
8. Rollout² 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.: ą 0.009 (-0.884...-0.867) - [0.0%]
Duration: 3 minutes 08 seconds
9. Rollout² 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.: ą 0.009 (-0.897...-0.880) - [0.0%]
Duration: 3 minutes 24 seconds
10. Rollout² 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.: ą 0.008 (-0.898...-0.881) - [0.0%]
Duration: 5 minutes 00 second
11. Rollout² 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.: ą 0.008 (-0.901...-0.885) - [0.0%]
Duration: 4 minutes 43 seconds

¹ 15552 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

² 2592 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Improving white distribution raises relative equity of stepping up.

White is Player 2

score: 0
pip: 126

Unlimited Game
Jacoby

pip: 146
score: 0

Blue is Player 1

XGID=---B--C-BAAAcD--bccd----A-:0:0:1:33:0:0:1:0:10
Blue to play 33

1. Rollout¹ 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.: ą 0.003 (-0.975...-0.969) - [90.6%]
Duration: 29 minutes 37 seconds
2. Rollout¹ 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.: ą 0.003 (-0.979...-0.972) - [9.4%]
Duration: 28 minutes 34 seconds
3. Rollout¹ 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.: ą 0.004 (-0.986...-0.979) - [0.0%]
Duration: 25 minutes 18 seconds
4. Rollout¹ 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.: ą 0.003 (-0.988...-0.981) - [0.0%]
Duration: 31 minutes 05 seconds

¹ 15552 Games rolled with Variance Reduction.
Dice Seed: 40238487
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Messages In This Thread

501 Essential Backgammon Problems #104
Igor -- Tuesday, 1 October 2013, at 2:43 a.m.
- 501 Essential Backgammon Problems #104
  Daniel Murphy -- Tuesday, 1 October 2013, at 3:31 a.m.
- 501 Essential Backgammon Problems #104
  ah_clem -- Tuesday, 1 October 2013, at 11:42 a.m.
- 501 Essential Backgammon Problems #104
  Taper_Mike -- Tuesday, 1 October 2013, at 1:58 p.m.
- 501 Essential Backgammon Problems #104 -- Rollout + Variants
  Igor -- Thursday, 3 October 2013, at 2:27 p.m.

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