FOUR SCORE Position, (Corrected) Rollouts for Fetching 55

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FOUR SCORE Position, (Corrected) Rollouts for Fetching 55

Posted By: Nack Ballard
Date: Thursday, 28 February 2019, at 10:20 a.m.

In Response To: FOUR SCORE Position, Rollouts for Fetching 55 (Nack Ballard)

White is Player 2

score: 0
pip: 137

Unlimited Game
Jacoby Beaver

pip: 143
score: 0

Blue is Player 1

XGID=-a--BCBB--AAbBca-a-cbb-AA-:0:0:1:55:0:0:3:0:10
Blue to play 55

You have the Blue checkers. How do you play 55, for...
.....(1) Money ?
.....(2) DMP ?
.....(3) Gammon Save ?
.....(4) Gammon Go ?

Thanks to Leo Beuno for his keen observations.
Below is a nacbrac summary of the rollouts (one line for each score).
.........m[p A10 C19 P25 J28 F31 R60 D116 f118] "<=237*15 10 5*1
..........d[P C11 p14 F22 J29 R49 f54 D84 c102 A116] <10*7 5*1
..........s[C P34 p51 F55 f92 R100 A109 c124] "<5***1
..........g[J A156 p164 D200 F252 C254 P259 R65] "<5**1
Key:..A (Attack) = 7/2(2) 6/1*(2), C (Cross) = 23/13 11/6 10/5, c = 23/13 7/2(2), D (2:1:1 Down) = 13/8(2) 11/1*, F (2:1:1 Field) = 23/13 13/8 11/6, f = 23/13 13/8 10/5, J (1:2:1 Jump) = 13/8 7/2(2) 6/1*), P (Point) = 23/8 13/8, p = 13/3(2), R (2:1:1 Run) = 23/13 11/1*.
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 a "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 [sqrt19 + sqrt 11*20/9 + sqrt34*10/7 + sqrt 156*10/7] = 31.20, a new record! 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, 52, 31 and 65.
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 adjust from there.
Detailed rollout results appear below (this time with the correct Gammon go diagram).
Nack

Money

White is Player 2

score: 0
pip: 137

Unlimited Game
Jacoby Beaver

pip: 143
score: 0

Blue is Player 1

XGID=-a--BCBB--AAbBca-a-cbb-AA-:0:0:1:55:0:0:3:0:10
.32S-43H-31H-32S-42P-64H-65R-53X-51@-32S-64H-F-
-52R-65R-43D-62H-21H-51Z-11N-31P-51c-62P-55

1. Rollout¹ 13/3(2) eq: +0.267
Player:
Opponent: 55.03% (G:24.63% B:0.84%)
44.97% (G:13.29% B:0.88%) Conf.: � 0.001 (+0.265...+0.268) - [100.0%]
Duration: 10 hours 38 minutes
2. Rollout¹ 7/2(2) 6/1*(2) eq: +0.257 (-0.010)
Player:
Opponent: 49.58% (G:30.79% B:0.69%)
50.42% (G:15.85% B:1.26%) Conf.: � 0.001 (+0.256...+0.258) - [0.0%]
Duration: 4 hours 31 minutes
3. Rollout² 23/13 11/6 10/5 eq: +0.248 (-0.019)
Player:
Opponent: 55.15% (G:20.45% B:0.68%)
44.85% (G:10.29% B:0.41%) Conf.: � 0.004 (+0.244...+0.252) - [0.0%]
Duration: 1 hour 14 minutes
4. Rollout³ 23/8 13/8 eq: +0.241 (-0.025)
Player:
Opponent: 55.85% (G:19.65% B:1.10%)
44.15% (G:12.89% B:0.77%) Conf.: � 0.006 (+0.235...+0.247) - [0.0%]
Duration: 1 hour 00 minute
5. Rollout⁴ 11/1* 7/2(2) eq: +0.238 (-0.028)
Player:
Opponent: 53.87% (G:33.78% B:1.16%)
46.13% (G:15.11% B:1.13%) Conf.: � 0.005 (+0.233...+0.244) - [0.0%]
Duration: 13 minutes 00 second
6. Rollout⁴ 23/8 11/6 eq: +0.236 (-0.031)
Player:
Opponent: 54.93% (G:20.52% B:0.82%)
45.07% (G:12.21% B:0.59%) Conf.: � 0.008 (+0.227...+0.244) - [0.0%]
Duration: 26 minutes 30 seconds
7. Rollout⁴ 23/13 11/1* eq: +0.207 (-0.060)
Player:
Opponent: 53.13% (G:21.66% B:0.59%)
46.87% (G:13.55% B:0.71%) Conf.: � 0.007 (+0.200...+0.214) - [0.0%]
Duration: 22 minutes 05 seconds
8. Rollout⁵ 13/8(2) 11/1* eq: +0.150 (-0.116)
Player:
Opponent: 51.12% (G:26.29% B:1.10%)
48.88% (G:15.78% B:1.11%) Conf.: � 0.012 (+0.138...+0.163) - [0.0%]
Duration: 3 minutes 09 seconds
9. Rollout⁵ 23/8 10/5 eq: +0.148 (-0.119)
Player:
Opponent: 52.95% (G:20.14% B:0.91%)
47.05% (G:13.32% B:0.69%) Conf.: � 0.015 (+0.133...+0.163) - [0.0%]
Duration: 4 minutes 15 seconds

¹ 237168 Games rolled with Variance Reduction.
Dice Seed: 77188235
Moves: 3-ply, cube decisions: XG Roller

² 15552 Games rolled with Variance Reduction.
Dice Seed: 77188235
Moves: 3-ply, cube decisions: XG Roller

³ 10368 Games rolled with Variance Reduction.
Dice Seed: 77188235
Moves: 3-ply, cube decisions: XG Roller

⁴ 5184 Games rolled with Variance Reduction.
Dice Seed: 77188235
Moves: 3-ply, cube decisions: XG Roller

⁵ 1296 Games rolled with Variance Reduction.
Dice Seed: 77188235
Moves: 3-ply, cube decisions: XG Roller

DMP

White is Player 2

score: 0
pip: 137

1 point match

pip: 143
score: 0

Blue is Player 1

XGID=-a--BCBB--AAbBca-a-cbb-AA-:0:0:1:55:0:0:0:1:10
Blue to play 55

1. Rollout¹ 23/8 13/8 eq: +0.114
Player:
Opponent: 55.69% (G:22.15% B:2.78%)
44.31% (G:14.08% B:1.95%) Conf.: � 0.002 (+0.112...+0.116) - [100.0%]
Duration: 1 hour 01 minute
2. Rollout¹ 23/13 11/6 10/5 eq: +0.103 (-0.011)
Player:
Opponent: 55.17% (G:21.17% B:1.38%)
44.83% (G:9.92% B:0.87%) Conf.: � 0.002 (+0.102...+0.105) - [0.0%]
Duration: 52 minutes 28 seconds
3. Rollout² 13/3(2) eq: +0.100 (-0.014)
Player:
Opponent: 54.98% (G:25.11% B:2.07%)
45.02% (G:13.45% B:1.85%) Conf.: � 0.002 (+0.097...+0.102) - [0.0%]
Duration: 30 minutes 15 seconds
4. Rollout³ 23/8 11/6 eq: +0.092 (-0.022)
Player:
Opponent: 54.60% (G:23.00% B:2.16%)
45.40% (G:12.33% B:1.15%) Conf.: � 0.003 (+0.089...+0.095) - [0.0%]
Duration: 25 minutes 50 seconds
5. Rollout³ 11/1* 7/2(2) eq: +0.085 (-0.029)
Player:
Opponent: 54.23% (G:35.44% B:1.61%)
45.77% (G:15.64% B:2.98%) Conf.: � 0.003 (+0.082...+0.087) - [0.0%]
Duration: 25 minutes 55 seconds
6. Rollout⁴ 23/13 11/1* eq: +0.064 (-0.049)
Player:
Opponent: 53.22% (G:21.05% B:1.10%)
46.78% (G:14.64% B:1.73%) Conf.: � 0.005 (+0.059...+0.070) - [0.0%]
Duration: 6 minutes 20 seconds
7. Rollout⁴ 23/8 10/5 eq: +0.060 (-0.054)
Player:
Opponent: 53.00% (G:20.77% B:1.87%)
47.00% (G:13.60% B:1.46%) Conf.: � 0.005 (+0.055...+0.065) - [0.0%]
Duration: 5 minutes 49 seconds
8. Rollout⁴ 13/8(2) 11/1* eq: +0.030 (-0.084)
Player:
Opponent: 51.51% (G:27.41% B:2.18%)
48.49% (G:16.44% B:3.08%) Conf.: � 0.006 (+0.024...+0.036) - [0.0%]
Duration: 6 minutes 07 seconds
9. Rollout⁴ 23/13 7/2(2) eq: +0.012 (-0.102)
Player:
Opponent: 50.58% (G:19.67% B:1.16%)
49.42% (G:12.30% B:1.06%) Conf.: � 0.005 (+0.007...+0.016) - [0.0%]
Duration: 5 minutes 19 seconds
10. Rollout⁴ 7/2(2) 6/1*(2) eq: -0.002 (-0.116)
Player:
Opponent: 49.89% (G:31.79% B:0.36%)
50.11% (G:14.78% B:2.02%) Conf.: � 0.005 (-0.007...+0.003) - [0.0%]
Duration: 5 minutes 07 seconds

¹ 10368 Games rolled with Variance Reduction.
Dice Seed: 36223632
Moves: 3-ply, cube decisions: XG Roller

² 7776 Games rolled with Variance Reduction.
Dice Seed: 36223632
Moves: 3-ply, cube decisions: XG Roller

³ 5184 Games rolled with Variance Reduction.
Dice Seed: 36223632
Moves: 3-ply, cube decisions: XG Roller

⁴ 1296 Games rolled with Variance Reduction.
Dice Seed: 36223632
Moves: 3-ply, cube decisions: XG Roller

Gammon Save

White is Player 2

score: 0
pip: 137

2 point match
Crawford

pip: 143
score: 1

Blue is Player 1

XGID=-a--BCBB--AAbBca-a-cbb-AA-:0:0:1:55:1:0:1:2:10
Blue to play 55

1. Rollout¹ 23/13 11/6 10/5 eq: -0.116
Player:
Opponent: 55.47% (G:21.52% B:1.77%)
44.53% (G:11.29% B:0.65%) Conf.: � 0.003 (-0.120...-0.113) - [100.0%]
Duration: 25 minutes 54 seconds
2. Rollout¹ 23/8 13/8 eq: -0.150 (-0.034)
Player:
Opponent: 55.28% (G:22.39% B:2.92%)
44.72% (G:12.79% B:1.44%) Conf.: � 0.004 (-0.154...-0.146) - [0.0%]
Duration: 29 minutes 54 seconds
3. Rollout¹ 13/3(2) eq: -0.168 (-0.051)
Player:
Opponent: 55.23% (G:25.27% B:2.25%)
44.77% (G:13.61% B:1.69%) Conf.: � 0.004 (-0.172...-0.164) - [0.0%]
Duration: 23 minutes 17 seconds
4. Rollout¹ 23/8 11/6 eq: -0.171 (-0.055)
Player:
Opponent: 54.52% (G:22.99% B:2.51%)
45.48% (G:13.09% B:1.07%) Conf.: � 0.004 (-0.175...-0.168) - [0.0%]
Duration: 26 minutes 20 seconds
5. Rollout² 23/8 10/5 eq: -0.209 (-0.092)
Player:
Opponent: 53.18% (G:21.76% B:2.49%)
46.82% (G:13.60% B:1.06%) Conf.: � 0.007 (-0.216...-0.201) - [0.0%]
Duration: 6 minutes 49 seconds
6. Rollout² 23/13 11/1* eq: -0.217 (-0.100)
Player:
Opponent: 53.88% (G:23.22% B:1.48%)
46.12% (G:14.71% B:1.00%) Conf.: � 0.007 (-0.223...-0.210) - [0.0%]
Duration: 7 minutes 30 seconds
7. Rollout² 11/1* 7/2(2) eq: -0.226 (-0.109)
Player:
Opponent: 54.56% (G:35.19% B:1.79%)
45.44% (G:15.86% B:2.55%) Conf.: � 0.007 (-0.233...-0.219) - [0.0%]
Duration: 6 minutes 15 seconds
8. Rollout² 23/13 7/2(2) eq: -0.241 (-0.124)
Player:
Opponent: 51.17% (G:19.99% B:1.09%)
48.83% (G:13.21% B:0.95%) Conf.: � 0.007 (-0.247...-0.234) - [0.0%]
Duration: 6 minutes 01 second

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 41518972
Moves: 3-ply, cube decisions: XG Roller

² 1296 Games rolled with Variance Reduction.
Dice Seed: 41518972
Moves: 3-ply, cube decisions: XG Roller

Gammon Go

White is Player 2

score: 1
pip: 137

2 point match
Crawford

pip: 143
score: 0

Blue is Player 1

XGID=-a--BCBB--AAbBca-a-cbb-AA-:0:0:1:55:0:1:1:2:10
Blue to play 55

1. Rollout¹ 11/1* 7/2(2) eq: +0.766
Player:
Opponent: 54.22% (G:34.10% B:1.43%)
45.78% (G:16.31% B:2.99%) Conf.: � 0.004 (+0.763...+0.770) - [100.0%]
Duration: 12 minutes 34 seconds
2. Rollout¹ 7/2(2) 6/1*(2) eq: +0.611 (-0.156)
Player:
Opponent: 49.66% (G:30.88% B:0.91%)
50.34% (G:14.47% B:2.12%) Conf.: � 0.004 (+0.607...+0.614) - [0.0%]
Duration: 11 minutes 57 seconds
3. Rollout¹ 13/3(2) eq: +0.602 (-0.164)
Player:
Opponent: 55.28% (G:24.83% B:1.17%)
44.72% (G:13.86% B:1.93%) Conf.: � 0.004 (+0.598...+0.606) - [0.0%]
Duration: 10 minutes 50 seconds
4. Rollout² 13/8(2) 11/1* eq: +0.566 (-0.200)
Player:
Opponent: 51.69% (G:26.61% B:1.92%)
48.31% (G:17.12% B:3.60%) Conf.: � 0.008 (+0.558...+0.574) - [0.0%]
Duration: 4 minutes 37 seconds
5. Rollout² 23/8 11/6 eq: +0.515 (-0.252)
Player:
Opponent: 54.80% (G:20.92% B:1.09%)
45.20% (G:13.14% B:1.07%) Conf.: � 0.008 (+0.507...+0.522) - [0.0%]
Duration: 4 minutes 08 seconds
6. Rollout² 23/13 11/6 10/5 eq: +0.512 (-0.254)
Player:
Opponent: 55.15% (G:20.47% B:0.84%)
44.85% (G:10.97% B:0.98%) Conf.: � 0.007 (+0.506...+0.519) - [0.0%]
Duration: 3 minutes 57 seconds
7. Rollout² 23/8 13/8 eq: +0.508 (-0.259)
Player:
Opponent: 56.72% (G:18.68% B:1.26%)
43.28% (G:13.97% B:2.01%) Conf.: � 0.008 (+0.500...+0.516) - [0.0%]
Duration: 4 minutes 43 seconds
8. Rollout² 23/13 11/1* eq: +0.501 (-0.265)
Player:
Opponent: 52.54% (G:22.53% B:1.16%)
47.46% (G:14.99% B:2.33%) Conf.: � 0.007 (+0.495...+0.508) - [0.0%]
Duration: 4 minutes 51 seconds

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 41518972
Moves: 3-ply, cube decisions: XG Roller

² 1296 Games rolled with Variance Reduction.
Dice Seed: 41518972
Moves: 3-ply, cube decisions: XG Roller

Messages In This Thread

FOUR SCORE Position, Rollouts for Fetching 55
Nack Ballard -- Thursday, 28 February 2019, at 2:08 a.m.
- FOUR SCORE Position, Rollouts for Fetching 55
  Ray Kershaw -- Thursday, 28 February 2019, at 9:15 a.m.
  - Thanks! (Link to corrected post)
    Nack Ballard -- Thursday, 28 February 2019, at 10:27 a.m.
- FOUR SCORE Position, (Corrected) Rollouts for Fetching 55
  Nack Ballard -- Thursday, 28 February 2019, at 10:20 a.m.

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