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501 Essential Backgammon Problems #280 -- Rollout + Variants

Posted By: Igor
Date: Friday, 29 November 2013, at 7:07 p.m.

In Response To: 501 Essential Backgammon Problems #280 (Igor)

Robertie suggests not hitting since blue is outboarded. But we need to hit to win this game and by our next roll white is going to have a five point home board. Now is the time to take our chances.

 White is Player 2 score: 0 pip: 95 Unlimited GameJacoby pip: 129 score: 0 Blue is Player 1
XGID=---ACbBBC---Ba-----cBcbca-:1:1:1:25:0:0:1:0:10
Blue to play 25

1.Rollout120/13* eq: +0.131
 Player:Opponent: 50.79% (G:10.47% B:0.55%)49.21% (G:18.72% B:0.30%) Conf.: ± 0.008 (+0.123...+0.139) - [100.0%]Duration: 5 minutes 25 seconds
2.Rollout18/3 4/2eq: +0.083 (-0.048)
 Player:Opponent: 46.91% (G:8.57% B:0.29%)53.09% (G:11.02% B:0.20%) Conf.: ± 0.005 (+0.078...+0.088) - [0.0%]Duration: 4 minutes 03 seconds
1 2592 Games rolled with Variance Reduction.
Dice Seed: 32271713
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Naturally, if white had a five point board now hitting would be a huge blunder.

 White is Player 2 score: 0 pip: 94 Unlimited GameJacoby pip: 129 score: 0 Blue is Player 1
XGID=---ACbBBC---Ba-----cBcbbb-:1:1:1:25:0:0:1:0:10
Blue to play 25

1.4-ply8/3 4/2eq: +0.051
 Player:Opponent: 46.33% (G:7.23% B:0.19%)53.67% (G:11.17% B:0.15%)
2.4-ply12/7 8/6eq: -0.113 (-0.163)
 Player:Opponent: 39.69% (G:5.69% B:0.20%)60.31% (G:10.43% B:0.11%)
3.4-ply20/13* eq: -0.159 (-0.210)
 Player:Opponent: 44.26% (G:7.17% B:0.29%)55.74% (G:26.98% B:0.63%)

eXtreme Gammon Version: 2.10

If we bring one of white builders from her 2pt back into play, hitting becomes barely wrong.

 White is Player 2 score: 0 pip: 99 Unlimited GameJacoby pip: 129 score: 0 Blue is Player 1
XGID=---ACbBBC---Ba-----dBcbba-:1:1:1:25:0:0:1:0:10
Blue to play 25

1.Rollout18/3 4/2eq: +0.043
 Player:Opponent: 45.52% (G:7.63% B:0.24%)54.48% (G:10.48% B:0.19%) Conf.: ± 0.002 (+0.041...+0.045) - [100.0%]Duration: 39 minutes 02 seconds
2.Rollout120/13* eq: +0.038 (-0.005)
 Player:Opponent: 48.61% (G:9.04% B:0.49%)51.39% (G:21.43% B:0.53%) Conf.: ± 0.002 (+0.036...+0.040) - [0.0%]Duration: 53 minutes 55 seconds
1 25920 Games rolled with Variance Reduction.
Dice Seed: 32271713
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

In the OP threes are duplicated for white to enter and hit our blot on the 3pt and cover her ace point. If we diversify white numbers, then the safe play gains in relative equity.

 White is Player 2 score: 0 pip: 94 Unlimited GameJacoby pip: 129 score: 0 Blue is Player 1
XGID=---ACbBBC---Ba-----cBbcca-:1:1:1:25:0:0:1:0:10
Blue to play 25

1.Rollout120/13* eq: +0.138
 Player:Opponent: 51.00% (G:10.69% B:0.58%)49.00% (G:19.64% B:0.32%) Conf.: ± 0.009 (+0.129...+0.147) - [100.0%]Duration: 2 minutes 36 seconds
2.Rollout18/3 4/2eq: +0.114 (-0.024)
 Player:Opponent: 48.26% (G:9.26% B:0.34%)51.74% (G:11.39% B:0.17%) Conf.: ± 0.007 (+0.107...+0.122) - [0.0%]Duration: 2 minutes 07 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 46722792
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Finally, if there is no blot in white's home board then the safe play is clearly best.

 White is Player 2 score: 0 pip: 101 Unlimited GameJacoby pip: 129 score: 0 Blue is Player 1
XGID=---ACbBBC---Ba-----dBccb--:1:1:1:25:0:0:1:0:10
Blue to play 25

1.Rollout18/3 4/2eq: +0.068
 Player:Opponent: 46.21% (G:7.79% B:0.26%)53.79% (G:9.70% B:0.21%) Conf.: ± 0.007 (+0.061...+0.075) - [100.0%]Duration: 2 minutes 04 seconds
2.Rollout120/13* eq: +0.015 (-0.053)
 Player:Opponent: 48.05% (G:8.21% B:0.41%)51.95% (G:21.53% B:0.59%) Conf.: ± 0.009 (+0.006...+0.023) - [0.0%]Duration: 2 minutes 42 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 32271713
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

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