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501 Essential Backgammon Problems #102 -- Rollout + Variants

Posted By: Igor
Date: Saturday, 21 September 2013, at 4:33 p.m.

In Response To: 501 Essential Backgammon Problems #102 (Igor)

Stepping up 24/22 with the deuce is clear. For the ace we have the following reasonable candidates:

1. Keep going with 22/21
2. Slot with 6/5
3. Step up with the second checker 24/23
4. Shuffle around with 11/10
5. Shuffle around with 8/7

Let's discard (4) right away since it does not improve our position one bit, but instead doubles the number of indirect shots at the blot.

Both (1) and (2) are big bold plays, but it looks like we are not at the point to attempt a desperate bold move to stay in the game. (See variants for that.)

That leaves (3) and (5) and most human players would choose the natural 24/23. However, XG almost prefers 8/7. The only explanation I can come up with is that 24/24 duplicates our aces, which we would like to use to make the 5pt using at least one checker from the heavy 6pt.

 White is Player 2 score: 0 pip: 144 Unlimited GameJacoby pip: 133 score: 0 Blue is Player 1
XGID=-b-B--EBC--Ab----bbeb---B-:0:0:1:12:0:0:1:0:10
Blue to play 12

1.Rollout124/22 8/7eq: -0.333
 Player:Opponent: 42.10% (G:13.44% B:0.93%)57.90% (G:19.87% B:1.00%) Conf.: ± 0.002 (-0.335...-0.330) - [99.9%]Duration: 1 hour 58 minutes
2.Rollout124/23 24/22eq: -0.338 (-0.005)
 Player:Opponent: 41.86% (G:13.15% B:0.99%)58.14% (G:19.82% B:0.95%) Conf.: ± 0.002 (-0.340...-0.336) - [0.1%]Duration: 2 hours 00 minute
3.Rollout224/21eq: -0.362 (-0.029)
 Player:Opponent: 41.34% (G:12.98% B:0.93%)58.66% (G:19.42% B:0.99%) Conf.: ± 0.008 (-0.370...-0.354) - [0.0%]Duration: 12 minutes 55 seconds
4.Rollout324/22 11/10eq: -0.387 (-0.055)
 Player:Opponent: 40.63% (G:12.61% B:0.84%)59.37% (G:20.19% B:0.99%) Conf.: ± 0.010 (-0.397...-0.377) - [0.0%]Duration: 6 minutes 42 seconds
5.Rollout324/22 6/5eq: -0.393 (-0.061)
 Player:Opponent: 40.79% (G:13.25% B:1.10%)59.21% (G:23.72% B:1.97%) Conf.: ± 0.012 (-0.405...-0.382) - [0.0%]Duration: 6 minutes 18 seconds
6.Rollout424/23 11/9eq: -0.425 (-0.092)
 Player:Opponent: 38.95% (G:12.74% B:0.96%)61.05% (G:20.18% B:0.99%) Conf.: ± 0.012 (-0.437...-0.413) - [0.0%]Duration: 3 minutes 33 seconds
7.Rollout47/5 6/5eq: -0.437 (-0.104)
 Player:Opponent: 38.32% (G:12.86% B:0.92%)61.68% (G:18.68% B:1.30%) Conf.: ± 0.015 (-0.452...-0.422) - [0.0%]Duration: 3 minutes 00 second
8.Rollout411/9 6/5eq: -0.462 (-0.129)
 Player:Opponent: 38.09% (G:12.32% B:0.81%)61.91% (G:20.05% B:1.48%) Conf.: ± 0.013 (-0.475...-0.448) - [0.0%]Duration: 2 minutes 55 seconds
9.Rollout411/9 8/7eq: -0.475 (-0.142)
 Player:Opponent: 37.45% (G:12.18% B:0.80%)62.55% (G:18.02% B:1.04%) Conf.: ± 0.015 (-0.489...-0.460) - [0.0%]Duration: 3 minutes 12 seconds
1 46656 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

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

4 1296 Games rolled with Variance Reduction.
Dice Seed: 93968057
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Let's see what happens if we improve white distribution.

 White is Player 2 score: 0 pip: 145 Unlimited GameJacoby pip: 133 score: 0 Blue is Player 1
XGID=-b-B--EBC--Ab----bcdb---B-:0:0:1:12:0:0:1:0:10
Blue to play 12

1.Rollout124/22 8/7eq: -0.445
 Player:Opponent: 39.37% (G:12.28% B:0.80%)60.63% (G:20.59% B:1.02%) Conf.: ± 0.004 (-0.449...-0.441) - [68.1%]Duration: 51 minutes 08 seconds
2.Rollout124/23 24/22eq: -0.446 (-0.001)
 Player:Opponent: 39.31% (G:11.97% B:0.85%)60.69% (G:21.18% B:1.02%) Conf.: ± 0.003 (-0.450...-0.443) - [31.9%]Duration: 49 minutes 03 seconds
3.Rollout224/22 6/5eq: -0.456 (-0.011)
 Player:Opponent: 39.09% (G:12.26% B:0.93%)60.91% (G:23.77% B:1.91%) Conf.: ± 0.006 (-0.462...-0.450) - [0.0%]Duration: 22 minutes 17 seconds
4.Rollout324/21eq: -0.463 (-0.018)
 Player:Opponent: 38.61% (G:12.17% B:0.94%)61.39% (G:20.30% B:1.01%) Conf.: ± 0.007 (-0.470...-0.456) - [0.0%]Duration: 11 minutes 55 seconds
1 20736 Games rolled with Variance Reduction.
Dice Seed: 23875395
Moves: 3-ply, cube decisions: XG Roller

2 10368 Games rolled with Variance Reduction.
Dice Seed: 23875395
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 23875395
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

We are definitely worse off, but not quite desperate enough to go for a bold play.

 White is Player 2 score: 0 pip: 147 Unlimited GameJacoby pip: 133 score: 0 Blue is Player 1
XGID=-b-B--EBC--Ab----cccb---B-:0:0:1:12:0:0:1:0:10
Blue to play 12

1.Rollout124/22 6/5eq: -0.468
 Player:Opponent: 38.48% (G:12.43% B:0.88%)61.52% (G:22.36% B:1.74%) Conf.: ± 0.003 (-0.471...-0.466) - [98.9%]Duration: 1 hour 53 minutes
2.Rollout124/21eq: -0.472 (-0.004)
 Player:Opponent: 37.95% (G:12.05% B:0.94%)62.05% (G:19.59% B:1.00%) Conf.: ± 0.002 (-0.475...-0.470) - [1.1%]Duration: 1 hour 51 minutes
3.Rollout224/22 8/7eq: -0.478 (-0.010)
 Player:Opponent: 38.19% (G:12.21% B:0.77%)61.81% (G:19.20% B:1.03%) Conf.: ± 0.004 (-0.483...-0.474) - [0.0%]Duration: 42 minutes 52 seconds
4.Rollout324/22 11/10eq: -0.497 (-0.029)
 Player:Opponent: 37.52% (G:11.65% B:0.81%)62.48% (G:19.22% B:1.03%) Conf.: ± 0.008 (-0.505...-0.490) - [0.0%]Duration: 14 minutes 04 seconds
5.Rollout424/23 24/22eq: -0.520 (-0.052)
 Player:Opponent: 37.38% (G:11.22% B:0.67%)62.62% (G:21.20% B:1.07%) Conf.: ± 0.013 (-0.534...-0.507) - [0.0%]Duration: 3 minutes 35 seconds
1 46656 Games rolled with Variance Reduction.
Dice Seed: 56773318
Moves: 3-ply, cube decisions: XG Roller

2 15552 Games rolled with Variance Reduction.
Dice Seed: 56773318
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 56773318
Moves: 3-ply, cube decisions: XG Roller

4 1296 Games rolled with Variance Reduction.
Dice Seed: 56773318
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Now is the time to go for the bold play. Half-measures no longer cut it.

 White is Player 2 score: 0 pip: 148 Unlimited GameJacoby pip: 133 score: 0 Blue is Player 1
XGID=-b-B--EBC--Ab---abccb---B-:0:0:1:12:0:0:1:0:10
Blue to play 12

1.Rollout124/22 6/5eq: -0.542
 Player:Opponent: 37.25% (G:12.50% B:1.04%)62.75% (G:26.03% B:2.54%) Conf.: ± 0.012 (-0.554...-0.530) - [100.0%]Duration: 13 minutes 10 seconds
2.Rollout124/21eq: -0.573 (-0.031)
 Player:Opponent: 35.08% (G:11.53% B:1.03%)64.92% (G:20.69% B:1.08%) Conf.: ± 0.007 (-0.580...-0.565) - [0.0%]Duration: 11 minutes 47 seconds
3.Rollout224/22 8/7eq: -0.587 (-0.045)
 Player:Opponent: 35.52% (G:11.34% B:0.80%)64.48% (G:20.54% B:1.12%) Conf.: ± 0.010 (-0.598...-0.577) - [0.0%]Duration: 6 minutes 52 seconds
4.Rollout224/22 11/10eq: -0.597 (-0.055)
 Player:Opponent: 34.78% (G:10.91% B:0.80%)65.22% (G:20.52% B:1.13%) Conf.: ± 0.009 (-0.606...-0.587) - [0.0%]Duration: 6 minutes 16 seconds
5.Rollout324/23 24/22eq: -0.617 (-0.075)
 Player:Opponent: 34.54% (G:10.72% B:0.75%)65.46% (G:20.77% B:1.02%) Conf.: ± 0.014 (-0.631...-0.603) - [0.0%]Duration: 3 minutes 17 seconds
1 5184 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

3 1296 Games rolled with Variance Reduction.
Dice Seed: 26837084
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

Still bold time, but now the slotting play clearly stands out; not only are we looking for a better anchor, but we must also try to counterprime white.

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