Four Score position with 64

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Four Score position with 64

Posted By: Nack Ballard
Date: Tuesday, 4 July 2017, at 2:15 a.m.

The original thread was initiated by Paul Weaver (a.k.a. "Wally Peever") on June 14th, in which he features an interesting position with two different best plays at the four main scores, and a third different best play at –2–4.
Paul's position inspired my variant (copied below), which is an R4 (real four-score position) and corrects a slight flaw by denying Blue a Money double before the roll. White owns her 12pt and 11pt (instead of her midpoint plus 10pt and 6pt spares) and her 2pt (instead of her 3pt).
[I was unable to match a fifth different best play with a fifth score. The closest is J (Jump, 10/6 7/1*), which rolls within .006 at c6 (Crawford, opp needs 6).]
The power rating for this R4 is [sqrt 21 + sqrt 13*20/9 + sqrt 10*10/7 + sqrt 72*10/7] = 23.88. To compare to the power ratings of other R4's, click here and scroll to the bottom. Also not yet included in that consolidation are R4's with rolls of 41 and 43.
Detailed rollout results follow (all with 3-ply checker play, XGR cube).
Nack
Money

White is Player 2

score: 0
pip: 128

Unlimited Game
Jacoby Beaver

pip: 108
score: 0

Blue is Player 1

XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:46:0:0:3:0:10
53P-51S-62R-44O-54@-51U-11N-31U-11I-31-64H-21H-41U-66J-
-54S-65S-63P-41U-41R-21H-21Z-65H-54R-65H-21Z-54@-11d-64
Perfectly played Money sequence (Nactation)

1. Rollout¹ 9/5 7/1* eq: +0.191
Player:
Opponent: 49.65% (G:19.97% B:0.16%)
50.35% (G:7.85% B:0.29%) Conf.: ± 0.003 (+0.188...+0.194) - [100.0%]
Duration: 13 minutes 55 seconds
2. Rollout¹ 20/16 7/1* eq: +0.169 (-0.021)
Player:
Opponent: 50.02% (G:23.78% B:0.48%)
49.98% (G:19.92% B:2.51%) Conf.: ± 0.002 (+0.167...+0.171) - [0.0%]
Duration: 6 minutes 04 seconds
3. Rollout² 7/1* 6/2 eq: +0.097 (-0.094)
Player:
Opponent: 50.48% (G:18.58% B:0.19%)
49.52% (G:8.45% B:0.45%) Conf.: ± 0.008 (+0.089...+0.105) - [0.0%]
Duration: 22 minutes 16 seconds
4. Rollout² 10/6 7/1* eq: +0.051 (-0.140)
Player:
Opponent: 49.73% (G:16.31% B:0.20%)
50.27% (G:7.29% B:0.36%) Conf.: ± 0.006 (+0.045...+0.057) - [0.0%]
Duration: 21 minutes 17 seconds
5. Rollout² 10/4 7/3 eq: +0.010 (-0.181)
Player:
Opponent: 49.61% (G:12.29% B:0.14%)
50.39% (G:6.82% B:0.32%) Conf.: ± 0.006 (+0.004...+0.016) - [0.0%]
Duration: 21 minutes 04 seconds

¹ 10368 Games rolled with Variance Reduction.
Dice Seed: 85506921
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 85506921
Moves: 3-ply, cube decisions: XG Roller

DMP

White is Player 2

score: 0
pip: 128

1 point match

pip: 108
score: 0

Blue is Player 1

XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:0:0:0:1:10
Blue to play 64

1. Rollout¹ 7/1* 6/2 eq: +0.006
Player:
Opponent: 50.32% (G:17.83% B:0.29%)
49.68% (G:7.90% B:0.54%) Conf.: ± 0.002 (+0.004...+0.009) - [100.0%]
Duration: 16 minutes 10 seconds
2. Rollout¹ 9/5 7/1* eq: -0.006 (-0.013)
Player:
Opponent: 49.69% (G:18.73% B:0.32%)
50.31% (G:8.08% B:0.44%) Conf.: ± 0.002 (-0.008...-0.004) - [0.0%]
Duration: 17 minutes 35 seconds
3. Rollout¹ 10/4 7/3 eq: -0.009 (-0.015)
Player:
Opponent: 49.57% (G:11.43% B:0.22%)
50.43% (G:5.44% B:0.30%) Conf.: ± 0.002 (-0.011...-0.007) - [0.0%]
Duration: 14 minutes 38 seconds
4. Rollout¹ 20/16 7/1* eq: -0.009 (-0.016)
Player:
Opponent: 49.54% (G:23.19% B:0.75%)
50.46% (G:19.39% B:2.65%) Conf.: ± 0.002 (-0.011...-0.007) - [0.0%]
Duration: 17 minutes 37 seconds
5. Rollout¹ 10/6 7/1* eq: -0.009 (-0.016)
Player:
Opponent: 49.53% (G:15.37% B:0.30%)
50.47% (G:6.76% B:0.37%) Conf.: ± 0.002 (-0.012...-0.007) - [0.0%]
Duration: 15 minutes 25 seconds

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 37357246
Moves: 3-ply, cube decisions: XG Roller

Gammon Save

White is Player 2

score: 0
pip: 128

2 point match
Crawford

pip: 108
score: 1

Blue is Player 1

XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:1:0:1:2:10
Blue to play 64

1. Rollout¹ 10/4 7/3 eq: -0.144
Player:
Opponent: 50.28% (G:13.49% B:0.33%)
49.72% (G:7.47% B:0.44%) Conf.: ± 0.001 (-0.145...-0.143) - [100.0%]
Duration: 1 hour 28 minutes
2. Rollout¹ 10/6 7/1* eq: -0.154 (-0.010)
Player:
Opponent: 50.13% (G:16.23% B:0.32%)
49.87% (G:7.81% B:0.49%) Conf.: ± 0.001 (-0.155...-0.152) - [0.0%]
Duration: 1 hour 44 minutes
3. Rollout² 7/1* 6/2 eq: -0.162 (-0.018)
Player:
Opponent: 50.87% (G:18.09% B:0.32%)
49.13% (G:8.97% B:0.57%) Conf.: ± 0.003 (-0.165...-0.159) - [0.0%]
Duration: 12 minutes 35 seconds
4. Rollout² 9/3 7/3 eq: -0.169 (-0.025)
Player:
Opponent: 49.45% (G:13.65% B:0.48%)
50.55% (G:7.91% B:0.49%) Conf.: ± 0.003 (-0.172...-0.166) - [0.0%]
Duration: 10 minutes 27 seconds
5. Rollout² 10/4 9/5 eq: -0.172 (-0.028)
Player:
Opponent: 48.54% (G:15.45% B:0.29%)
51.46% (G:7.12% B:0.37%) Conf.: ± 0.003 (-0.174...-0.169) - [0.0%]
Duration: 12 minutes 30 seconds
6. Rollout² 9/5 7/1* eq: -0.177 (-0.033)
Player:
Opponent: 50.63% (G:20.66% B:0.49%)
49.37% (G:9.48% B:0.67%) Conf.: ± 0.003 (-0.180...-0.174) - [0.0%]
Duration: 12 minutes 43 seconds

¹ 41472 Games rolled with Variance Reduction.
Dice Seed: 85506921
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 85506921
Moves: 3-ply, cube decisions: XG Roller

Gammon Go

White is Player 2

score: 1
pip: 128

2 point match
Crawford

pip: 108
score: 0

Blue is Player 1

XGID=-aBBB-DA-AA--bbb--bbBb-b--:0:0:1:64:0:1:1:2:10
Blue to play 64

1. Rollout¹ 20/16 7/1* eq: +0.455
Player:
Opponent: 50.01% (G:22.76% B:0.65%)
49.99% (G:18.18% B:2.30%) Conf.: ± 0.004 (+0.451...+0.459) - [100.0%]
Duration: 16 minutes 40 seconds
2. Rollout¹ 9/5 7/1* eq: +0.384 (-0.072)
Player:
Opponent: 49.72% (G:19.47% B:0.31%)
50.28% (G:8.12% B:0.43%) Conf.: ± 0.004 (+0.380...+0.387) - [0.0%]
Duration: 16 minutes 15 seconds
3. Rollout¹ 7/1* 6/2 eq: +0.368 (-0.087)
Player:
Opponent: 50.56% (G:17.84% B:0.22%)
49.44% (G:8.00% B:0.69%) Conf.: ± 0.004 (+0.364...+0.372) - [0.0%]
Duration: 15 minutes 23 seconds
4. Rollout¹ 10/6 7/1* eq: +0.314 (-0.141)
Player:
Opponent: 49.99% (G:15.71% B:0.24%)
50.01% (G:6.82% B:0.51%) Conf.: ± 0.004 (+0.310...+0.318) - [0.0%]
Duration: 14 minutes 57 seconds

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 85506921
Moves: 3-ply, cube decisions: XG Roller

Messages In This Thread

Four Score position with 64
Nack Ballard -- Tuesday, 4 July 2017, at 2:15 a.m.
- Correction (power rating)
  Nack Ballard -- Tuesday, 4 July 2017, at 2:53 a.m.
- Four Score position with 64
  Paul Weaver -- Tuesday, 4 July 2017, at 12:42 p.m.
  - Cube location
    Nack Ballard -- Tuesday, 4 July 2017, at 9:29 p.m.

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