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FOUR SCORE position, Rollouts for Thrilling 31

Posted By: Nack Ballard
Date: Tuesday, 17 April 2018, at 7:10 a.m.

Thanks to Stick for his illuminating comments. He gave the correct plays at all four scores.

Below is a nacbrac summary of the rollouts (one line for each score).

.........m[N K26 P45 E94] "<=10*5
..........d[K P7 N15 E43] <62*5,.....d[K P7] ^12
..........s[E N42 K55 P101] "<5
..........g[P N16 K28... E160] "<5

Key:..E (Each) = 23/22 6/3, K (Kill) = 13/12* 13/10*, N (Near) = 13/12* 6/3, P (Point) = 8/5* 6/5.
Nactation tutorial ....nacbracs explanation

Each of the four main scores has a different best play. In fact, this is not only a T4 (technical four-score position). It is also an "R4" (real four-score position), meaning that for each of money, DMP, gammon save and gammon go, the best play clears its respective .010, .0045, .007 and .007 "tied" margin (compared to any play that is best at some other score).

The power rating for this R4 is [sqrt 26 + sqrt 7*20/9 + sqrt 42*10/7 + sqrt 16*10/7] = 21.57. To compare to the power ratings of other R4's, click here (scroll to the bottom). Also not yet included in that consolidation are R4's with rolls of 41, 43, 64, 44, 65, 21, 54 and 52.

[I have yet to construct R4's with rolls of 32, 42, 51, 61, 62 and 63. If you run across what appears to be a T3 or T4 position with one of these rolls, please let me know and perhaps I can tweak from there.]

Detailed rollout results follow.

Money

		White is Player 2 score: 0 pip: 160 Unlimited Game Jacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=--aAbaD-C-a-aE---a-bccAA--:0:0:1:31:0:0:3:0:10
.62S-64H-64@-41R-21H-65K-21-65D-52Z-11- -62R-44M-33R-43S-53R-41E-52R-62X-61U-62H- -63H-64H-F-43H-63-31H-52H-52P-31

1.	Rollout1	13/12* 6/3	eq: -0.008
	Player: Opponent: 50.13% (G:17.00% B:1.07%) 49.87% (G:18.15% B:0.98%) Conf.: ± 0.007 (-0.015...-0.001) - [100.0%] Duration: 2 hours 27 minutes
2.	Rollout1	13/12* 13/10*	eq: -0.033 (-0.026)
	Player: Opponent: 50.46% (G:16.00% B:0.86%) 49.54% (G:19.76% B:1.74%) Conf.: ± 0.007 (-0.041...-0.026) - [0.0%] Duration: 2 hours 36 minutes
3.	Rollout2	8/5* 6/5	eq: -0.053 (-0.045)
	Player: Opponent: 49.85% (G:17.99% B:1.18%) 50.15% (G:21.55% B:1.37%) Conf.: ± 0.013 (-0.066...-0.040) - [0.0%] Duration: 1 hour 15 minutes
4.	Rollout2	23/22 6/3	eq: -0.102 (-0.094)
	Player: Opponent: 48.15% (G:11.28% B:0.45%) 51.85% (G:15.17% B:0.52%) Conf.: ± 0.008 (-0.110...-0.094) - [0.0%] Duration: 1 hour 20 minutes
1 10368 Games rolled with Variance Reduction. Dice Seed: 1504617 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 1504617 Moves: 3-ply, cube decisions: XG Roller

DMP

		White is Player 2 score: 0 pip: 160 1 point match pip: 161 score: 0 Blue is Player 1
XGID=--aAbaD-C-a-aE---a-bccAA--:0:0:1:31:0:0:0:1:10
Blue to play 31

1.	Rollout1	13/12* 13/10*	eq: +0.008
	Player: Opponent: 50.41% (G:18.44% B:2.59%) 49.59% (G:22.04% B:5.45%) Conf.: ± 0.001 (+0.007...+0.009) - [100.0%] Duration: 9 hours 23 minutes
2.	Rollout1	8/5* 6/5	eq: +0.001 (-0.007)
	Player: Opponent: 50.05% (G:19.53% B:3.11%) 49.95% (G:24.37% B:4.80%) Conf.: ± 0.001 (0.000...+0.002) - [0.0%] Duration: 8 hours 12 minutes
3.	Rollout2	13/12* 6/3	eq: -0.006 (-0.014)
	Player: Opponent: 49.69% (G:20.00% B:3.28%) 50.31% (G:20.42% B:3.48%) Conf.: ± 0.003 (-0.010...-0.003) - [0.0%] Duration: 1 hour 16 minutes
4.	Rollout2	23/22 6/3	eq: -0.035 (-0.043)
	Player: Opponent: 48.24% (G:13.83% B:1.35%) 51.76% (G:18.05% B:1.85%) Conf.: ± 0.003 (-0.038...-0.032) - [0.0%] Duration: 1 hour 00 minute
1 62208 Games rolled with Variance Reduction. Dice Seed: 20417990 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 20417990 Moves: 3-ply, cube decisions: XG Roller

Gammon Save

		White is Player 2 score: 0 pip: 160 2 point match Crawford pip: 161 score: 1 Blue is Player 1
XGID=--aAbaD-C-a-aE---a-bccAA--:0:0:1:31:1:0:1:2:10
Blue to play 31

1.	Rollout1	23/22 6/3	eq: -0.334
	Player: Opponent: 47.16% (G:13.52% B:1.14%) 52.84% (G:13.88% B:1.15%) Conf.: ± 0.004 (-0.338...-0.330) - [100.0%] Duration: 1 hour 01 minute
2.	Rollout1	13/12* 6/3	eq: -0.376 (-0.042)
	Player: Opponent: 49.26% (G:20.74% B:3.04%) 50.74% (G:18.06% B:2.46%) Conf.: ± 0.005 (-0.381...-0.371) - [0.0%] Duration: 1 hour 17 minutes
3.	Rollout1	13/12* 13/10*	eq: -0.389 (-0.055)
	Player: Opponent: 49.80% (G:18.95% B:2.27%) 50.20% (G:19.27% B:4.36%) Conf.: ± 0.006 (-0.395...-0.384) - [0.0%] Duration: 1 hour 29 minutes
4.	Rollout1	8/5* 6/5	eq: -0.435 (-0.101)
	Player: Opponent: 48.94% (G:19.56% B:3.15%) 51.06% (G:20.70% B:3.87%) Conf.: ± 0.005 (-0.441...-0.430) - [0.0%] Duration: 1 hour 16 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 836695 Moves: 3-ply, cube decisions: XG Roller

Gammon Go

		White is Player 2 score: 1 pip: 160 2 point match Crawford pip: 161 score: 0 Blue is Player 1
XGID=--aAbaD-C-a-aE---a-bccAA--:0:0:1:31:0:1:1:2:10
Blue to play 31

1.	Rollout1	8/5* 6/5	eq: +0.354
	Player: Opponent: 50.48% (G:17.22% B:3.29%) 49.52% (G:24.60% B:4.62%) Conf.: ± 0.004 (+0.350...+0.358) - [100.0%] Duration: 2 hours 16 minutes
2.	Rollout1	13/12* 6/3	eq: +0.338 (-0.016)
	Player: Opponent: 50.50% (G:16.37% B:3.30%) 49.50% (G:20.24% B:3.47%) Conf.: ± 0.003 (+0.334...+0.341) - [0.0%] Duration: 2 hours 19 minutes
3.	Rollout2	13/12* 13/10*	eq: +0.325 (-0.028)
	Player: Opponent: 50.56% (G:15.71% B:2.86%) 49.44% (G:22.58% B:5.28%) Conf.: ± 0.005 (+0.320...+0.331) - [0.0%] Duration: 1 hour 12 minutes
4.	Rollout2	13/10* 3/2*	eq: +0.265 (-0.089)
	Player: Opponent: 48.52% (G:14.71% B:2.08%) 51.48% (G:23.37% B:4.78%) Conf.: ± 0.005 (+0.260...+0.270) - [0.0%] Duration: 46 minutes 17 seconds
5.	Rollout2	13/10* 6/5*	eq: +0.264 (-0.090)
	Player: Opponent: 47.87% (G:15.31% B:2.96%) 52.13% (G:28.80% B:7.43%) Conf.: ± 0.006 (+0.258...+0.269) - [0.0%] Duration: 50 minutes 28 seconds
6.	Rollout2	13/12* 8/5*	eq: +0.242 (-0.111)
	Player: Opponent: 47.19% (G:14.93% B:2.97%) 52.81% (G:27.97% B:7.31%) Conf.: ± 0.006 (+0.237...+0.248) - [0.0%] Duration: 51 minutes 20 seconds
7.	Rollout2	23/22 6/3	eq: +0.194 (-0.160)
	Player: Opponent: 48.72% (G:10.99% B:1.15%) 51.28% (G:18.54% B:1.84%) Conf.: ± 0.004 (+0.190...+0.198) - [0.0%] Duration: 36 minutes 00 second
1 10368 Games rolled with Variance Reduction. Dice Seed: 1659206 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 1659206 Moves: 3-ply, cube decisions: XG Roller

-----------------------------------------------------------------------------------------------------------------------

		White is Player 2 score: 1 pip: 148 2 point match Crawford pip: 161 score: 0 Blue is Player 1
XGID=---AbaD-C-a-aE---c-bbcAA--:0:0:1:31:0:1:1:2:10
Gammon Go, 3-ply

1.	Rollout1	8/5* 6/5	eq: +0.0712
	Player: Opponent: 42.26% (G:11.30% B:1.52%) 57.74% (G:29.18% B:5.42%) Conf.: ±0.0007 (+0.0706...+0.0719) - [100.0%] Duration: 18 hours 29 minutes
2.	Rollout1	13/12* 13/10*	eq: +0.0640 (-0.0072)
	Player: Opponent: 43.03% (G:10.17% B:1.24%) 56.97% (G:28.73% B:6.50%) Conf.: ±0.0007 (+0.0633...+0.0648) - [0.0%] Duration: 21 hours 02 minutes
3.	Rollout2	13/12* 6/3	eq: +0.0469 (-0.0243)
	Player: Opponent: 42.80% (G:9.55% B:1.11%) 57.20% (G:25.11% B:4.01%) Conf.: ±0.0020 (+0.0449...+0.0489) - [0.0%] Duration: 57 minutes 49 seconds
4.	Rollout3	13/10* 6/5*	eq: +0.0067 (-0.0645)
	Player: Opponent: 40.57% (G:9.77% B:1.32%) 59.43% (G:34.82% B:8.59%) Conf.: ±0.0050 (+0.0017...+0.0118) - [0.0%] Duration: 31 minutes 34 seconds
5.	Rollout4	13/12* 8/5*	eq: -0.0257 (-0.0969)
	Player: Opponent: 39.19% (G:9.52% B:1.26%) 60.81% (G:35.38% B:9.59%) Conf.: ±0.0049 (-0.0306...-0.0208) - [0.0%] Duration: 58 minutes 21 seconds
6.	Rollout4	23/22 6/3	eq: -0.0658 (-0.1370)
	Player: Opponent: 39.24% (G:7.47% B:0.57%) 60.76% (G:20.02% B:2.01%) Conf.: ±0.0034 (-0.0692...-0.0624) - [0.0%] Duration: 41 minutes 42 seconds
1 221616 Games rolled with Variance Reduction. Dice Seed: 13974616 Moves: 3-ply, cube decisions: XG Roller 2 20736 Games rolled with Variance Reduction. Dice Seed: 13974616 Moves: 3-ply, cube decisions: XG Roller 3 5184 Games rolled with Variance Reduction. Dice Seed: 13974616 Moves: 3-ply, cube decisions: XG Roller 4 5184 Games rolled with Variance Reduction. Dice Seed: 61808798 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 1 pip: 148 2 point match Crawford pip: 161 score: 0 Blue is Player 1
XGID=---AbaD-C-a-aE---c-bbcAA--:0:0:1:31:0:1:1:2:10
Gammon Go, 4-ply

1.	Rollout1	8/5* 6/5	eq: +0.0728
	Player: Opponent: 42.29% (G:11.36% B:1.54%) 57.71% (G:29.31% B:5.38%) Conf.: ±0.0004 (+0.0725...+0.0732) - [100.0%] Duration: 12 days 22 hours 37 minutes
2.	Rollout1	13/12* 13/10*	eq: +0.0661 (-0.0068)
	Player: Opponent: 43.10% (G:10.21% B:1.21%) 56.90% (G:28.69% B:6.39%) Conf.: ±0.0004 (+0.0657...+0.0665) - [0.0%] Duration: 15 days 06 hours 10 minutes
1 436852 Games rolled with Variance Reduction. Dice Seed: 85184203 Moves and cube decisions: 4-ply

Above is a variant position that does not quite qualify as an R4, at least not yet. The two rollouts (side-by-side, if your window is wide) are at Gammon Go. With 3-ply, the .0070 threshold appears to be met, though there is enough variance to perhaps reverse it. With 4-ply, the threshold is not yet met, though enough variance remains that it might be. As time permits, I will further extend the rollouts.

Below is a nacbrac summary of the rollouts of this variant at all four scores (one line for each score).

.........m[N K18 P47 E60] "<=33*5
..........d[K N10 P14 n48 E72] <12*5
..........s[E N118 K174 P190] "<5
..........g[P K7.2 N24... E137] "<221*20*5, .....d[K P6.8] ^436

Key:..E (Each) = 23/22 6/3, K (Kill) = 13/12* 13/10*, N (Near) = 13/12* 6/3, P (Point) = 8/5* 6/5.
Nactation tutorial ....nacbracs explanation

Nack

Messages In This Thread

• FOUR SCORE position, Rollouts for Thrilling 31
  Nack Ballard -- Tuesday, 17 April 2018, at 7:10 a.m.
  • FOUR SCORE position, Rollouts for Thrilling 31
    hominid -- Tuesday, 17 April 2018, at 9:47 p.m.