501 Essential Backgammon Problems #102 -- Rollout + Variants

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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:

Keep going with 22/21

Slot with 6/5

Step up with the second checker 24/23

Shuffle around with 11/10

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 Game
Jacoby

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. Rollout¹ 24/22 8/7 eq: -0.333
Player:
Opponent: 42.10% (G:13.44% B:0.93%)
57.90% (G:19.87% B:1.00%) Conf.: ą 0.002 (-0.335...-0.330) - [99.9%]
Duration: 1 hour 58 minutes
2. Rollout¹ 24/23 24/22 eq: -0.338 (-0.005)
Player:
Opponent: 41.86% (G:13.15% B:0.99%)
58.14% (G:19.82% B:0.95%) Conf.: ą 0.002 (-0.340...-0.336) - [0.1%]
Duration: 2 hours 00 minute
3. Rollout² 24/21 eq: -0.362 (-0.029)
Player:
Opponent: 41.34% (G:12.98% B:0.93%)
58.66% (G:19.42% B:0.99%) Conf.: ą 0.008 (-0.370...-0.354) - [0.0%]
Duration: 12 minutes 55 seconds
4. Rollout³ 24/22 11/10 eq: -0.387 (-0.055)
Player:
Opponent: 40.63% (G:12.61% B:0.84%)
59.37% (G:20.19% B:0.99%) Conf.: ą 0.010 (-0.397...-0.377) - [0.0%]
Duration: 6 minutes 42 seconds
5. Rollout³ 24/22 6/5 eq: -0.393 (-0.061)
Player:
Opponent: 40.79% (G:13.25% B:1.10%)
59.21% (G:23.72% B:1.97%) Conf.: ą 0.012 (-0.405...-0.382) - [0.0%]
Duration: 6 minutes 18 seconds
6. Rollout⁴ 24/23 11/9 eq: -0.425 (-0.092)
Player:
Opponent: 38.95% (G:12.74% B:0.96%)
61.05% (G:20.18% B:0.99%) Conf.: ą 0.012 (-0.437...-0.413) - [0.0%]
Duration: 3 minutes 33 seconds
7. Rollout⁴ 7/5 6/5 eq: -0.437 (-0.104)
Player:
Opponent: 38.32% (G:12.86% B:0.92%)
61.68% (G:18.68% B:1.30%) Conf.: ą 0.015 (-0.452...-0.422) - [0.0%]
Duration: 3 minutes 00 second
8. Rollout⁴ 11/9 6/5 eq: -0.462 (-0.129)
Player:
Opponent: 38.09% (G:12.32% B:0.81%)
61.91% (G:20.05% B:1.48%) Conf.: ą 0.013 (-0.475...-0.448) - [0.0%]
Duration: 2 minutes 55 seconds
9. Rollout⁴ 11/9 8/7 eq: -0.475 (-0.142)
Player:
Opponent: 37.45% (G:12.18% B:0.80%)
62.55% (G:18.02% B:1.04%) Conf.: ą 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 Game
Jacoby

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. Rollout¹ 24/22 8/7 eq: -0.445
Player:
Opponent: 39.37% (G:12.28% B:0.80%)
60.63% (G:20.59% B:1.02%) Conf.: ą 0.004 (-0.449...-0.441) - [68.1%]
Duration: 51 minutes 08 seconds
2. Rollout¹ 24/23 24/22 eq: -0.446 (-0.001)
Player:
Opponent: 39.31% (G:11.97% B:0.85%)
60.69% (G:21.18% B:1.02%) Conf.: ą 0.003 (-0.450...-0.443) - [31.9%]
Duration: 49 minutes 03 seconds
3. Rollout² 24/22 6/5 eq: -0.456 (-0.011)
Player:
Opponent: 39.09% (G:12.26% B:0.93%)
60.91% (G:23.77% B:1.91%) Conf.: ą 0.006 (-0.462...-0.450) - [0.0%]
Duration: 22 minutes 17 seconds
4. Rollout³ 24/21 eq: -0.463 (-0.018)
Player:
Opponent: 38.61% (G:12.17% B:0.94%)
61.39% (G:20.30% B:1.01%) Conf.: ą 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 Game
Jacoby

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. Rollout¹ 24/22 6/5 eq: -0.468
Player:
Opponent: 38.48% (G:12.43% B:0.88%)
61.52% (G:22.36% B:1.74%) Conf.: ą 0.003 (-0.471...-0.466) - [98.9%]
Duration: 1 hour 53 minutes
2. Rollout¹ 24/21 eq: -0.472 (-0.004)
Player:
Opponent: 37.95% (G:12.05% B:0.94%)
62.05% (G:19.59% B:1.00%) Conf.: ą 0.002 (-0.475...-0.470) - [1.1%]
Duration: 1 hour 51 minutes
3. Rollout² 24/22 8/7 eq: -0.478 (-0.010)
Player:
Opponent: 38.19% (G:12.21% B:0.77%)
61.81% (G:19.20% B:1.03%) Conf.: ą 0.004 (-0.483...-0.474) - [0.0%]
Duration: 42 minutes 52 seconds
4. Rollout³ 24/22 11/10 eq: -0.497 (-0.029)
Player:
Opponent: 37.52% (G:11.65% B:0.81%)
62.48% (G:19.22% B:1.03%) Conf.: ą 0.008 (-0.505...-0.490) - [0.0%]
Duration: 14 minutes 04 seconds
5. Rollout⁴ 24/23 24/22 eq: -0.520 (-0.052)
Player:
Opponent: 37.38% (G:11.22% B:0.67%)
62.62% (G:21.20% B:1.07%) Conf.: ą 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 Game
Jacoby

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. Rollout¹ 24/22 6/5 eq: -0.542
Player:
Opponent: 37.25% (G:12.50% B:1.04%)
62.75% (G:26.03% B:2.54%) Conf.: ą 0.012 (-0.554...-0.530) - [100.0%]
Duration: 13 minutes 10 seconds
2. Rollout¹ 24/21 eq: -0.573 (-0.031)
Player:
Opponent: 35.08% (G:11.53% B:1.03%)
64.92% (G:20.69% B:1.08%) Conf.: ą 0.007 (-0.580...-0.565) - [0.0%]
Duration: 11 minutes 47 seconds
3. Rollout² 24/22 8/7 eq: -0.587 (-0.045)
Player:
Opponent: 35.52% (G:11.34% B:0.80%)
64.48% (G:20.54% B:1.12%) Conf.: ą 0.010 (-0.598...-0.577) - [0.0%]
Duration: 6 minutes 52 seconds
4. Rollout² 24/22 11/10 eq: -0.597 (-0.055)
Player:
Opponent: 34.78% (G:10.91% B:0.80%)
65.22% (G:20.52% B:1.13%) Conf.: ą 0.009 (-0.606...-0.587) - [0.0%]
Duration: 6 minutes 16 seconds
5. Rollout³ 24/23 24/22 eq: -0.617 (-0.075)
Player:
Opponent: 34.54% (G:10.72% B:0.75%)
65.46% (G:20.77% B:1.02%) Conf.: ą 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.

Messages In This Thread

501 Essential Backgammon Problems #102
Igor -- Thursday, 19 September 2013, at 2:03 a.m.
- 501 Essential Backgammon Problems #102
  ah_clem -- Thursday, 19 September 2013, at 2:33 a.m.
- 501 Essential Backgammon Problems #102
  Taper_Mike -- Thursday, 19 September 2013, at 11:21 a.m.
- 501 Essential Backgammon Problems #102 -- Rollout + Variants
  Igor -- Saturday, 21 September 2013, at 4:33 p.m.
  - 501 Essential Backgammon Problems #102 -- Rollout + Variants
    Philippe Michel -- Saturday, 21 September 2013, at 7:20 p.m.
  - Hiding behind Jacoby
    Taper_Mike -- Tuesday, 24 September 2013, at 11:08 p.m.
    - Hiding behind Jacoby
      Daniel Murphy -- Wednesday, 25 September 2013, at 12:44 a.m.
      - 2nd roll that may be affected due to Jacoby
        David Presser -- Thursday, 26 September 2013, at 4:57 p.m.
    - Hiding behind Jacoby
      Bob Koca -- Wednesday, 25 September 2013, at 2:16 p.m.
    - Hiding behind Jacoby
      Igor -- Wednesday, 25 September 2013, at 10:14 p.m.
    - Hiding behind Jacoby
      Taper_Mike -- Thursday, 26 September 2013, at 10:24 a.m.

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