Thanks to respondents Fatboy, Michael, Mike Clapsadle, ah_clem and Phil Simborg for their insightful comments. In a bewildering position with six very plausible candidate plays, they parsed out the match score plays well on the whole (9 correct multiple-choice answers out of 17). Four out of five respondents supported the best money play, and four out of four correctly touted the best gammon go play.
Understandably, the biggest surprise was that H (Hit, 24/13*) is not best at any score. Three respondents projected H best at DMP, and one thought it best for money. The second biggest surprise was that neither anchoring play (on 18pt or 16pt) is best at gammon save.
Here is a nacbrac summary of the rollouts (one line for each score):
.........m[P H34 U37 S39 K41 @75] "<=5
..........d[U H15 P18 K19 @23 S26] "<=5
..........s[S U12 @15 P19 H38 K103] "<=10***5
..........g[K P25 H49 U64 S73 @81] "<=5
Key:..U (Up) = 24/18 23/18, @ (anchor) = 22/16 21/16, H (Hit) = 24/13*, S (Split-and-down) = 21/10, P (Point) = 11/5 10/5, K (Kill) = 10/4* 8/3*.....Nactation tutorial ....nacbracs explanation
As some of you may have guessed, 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 37 + sqrt 18*20/9 + sqrt 12*10/7 + sqrt 25*10/7] = 22.52. 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 and 64.
Detailed rollout results follow (all with 3-ply checker play, XGR cube).
Nack
Money
| 1. | Rollout1 | 11/5 10/5 | eq: -0.396 |
| Player:
Opponent: | 39.91% (G:13.88% B:0.61%)
60.09% (G:19.36% B:1.46%) | Conf.: ± 0.009 (-0.405...-0.387) - [100.0%]
Duration: 47 minutes 38 seconds |
|
| 2. | Rollout1 | 24/13* | eq: -0.430 (-0.034) |
| Player:
Opponent: | 40.02% (G:12.43% B:0.65%)
59.98% (G:20.93% B:1.45%) | Conf.: ± 0.009 (-0.439...-0.420) - [0.0%]
Duration: 58 minutes 23 seconds |
|
| 3. | Rollout1 | 24/18 23/18 | eq: -0.433 (-0.037) |
| Player:
Opponent: | 40.18% (G:10.42% B:0.45%)
59.82% (G:19.38% B:0.96%) | Conf.: ± 0.008 (-0.441...-0.424) - [0.0%]
Duration: 59 minutes 05 seconds |
|
| 4. | Rollout1 | 21/10 | eq: -0.435 (-0.039) |
| Player:
Opponent: | 39.23% (G:11.83% B:0.50%)
60.77% (G:17.90% B:1.11%) | Conf.: ± 0.009 (-0.444...-0.427) - [0.0%]
Duration: 56 minutes 08 seconds |
|
| 5. | Rollout1 | 10/4* 8/3* | eq: -0.437 (-0.041) |
| Player:
Opponent: | 39.65% (G:14.85% B:0.80%)
60.35% (G:24.40% B:2.24%) | Conf.: ± 0.008 (-0.445...-0.428) - [0.0%]
Duration: 42 minutes 38 seconds |
|
| 6. | Rollout1 | 22/16 21/16 | eq: -0.471 (-0.075) |
| Player:
Opponent: | 38.95% (G:10.94% B:0.43%)
61.05% (G:19.29% B:1.19%) | Conf.: ± 0.009 (-0.480...-0.462) - [0.0%]
Duration: 59 minutes 36 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 64925417
Moves: 3-ply, cube decisions: XG Roller
|
DMP
          
 
          
 | | White is Player 2
score: 0
pip: 158 | | 1 point match | pip: 171
score: 0
Blue is Player 1 |
|
| XGID=--Baa-C-B-ACda---c-bcAAAA-:0:0:1:65:0:0:0:1:10 |
| Blue to play 65 |
| 1. | Rollout1 | 24/18 23/18 | eq: -0.185 |
| Player:
Opponent: | 40.73% (G:11.65% B:1.25%)
59.27% (G:22.99% B:3.57%) | Conf.: ± 0.003 (-0.189...-0.182) - [100.0%]
Duration: 48 minutes 55 seconds |
|
| 2. | Rollout1 | 24/13* | eq: -0.200 (-0.015) |
| Player:
Opponent: | 39.99% (G:14.67% B:1.95%)
60.01% (G:24.14% B:4.56%) | Conf.: ± 0.003 (-0.204...-0.197) - [0.0%]
Duration: 56 minutes 24 seconds |
|
| 3. | Rollout1 | 11/5 10/5 | eq: -0.203 (-0.018) |
| Player:
Opponent: | 39.83% (G:15.56% B:1.80%)
60.17% (G:21.86% B:3.98%) | Conf.: ± 0.003 (-0.207...-0.200) - [0.0%]
Duration: 42 minutes 47 seconds |
|
| 4. | Rollout1 | 10/4* 8/3* | eq: -0.204 (-0.019) |
| Player:
Opponent: | 39.80% (G:16.48% B:2.74%)
60.20% (G:26.97% B:5.84%) | Conf.: ± 0.004 (-0.208...-0.200) - [0.0%]
Duration: 55 minutes 39 seconds |
|
| 5. | Rollout1 | 22/16 21/16 | eq: -0.208 (-0.023) |
| Player:
Opponent: | 39.58% (G:11.34% B:1.15%)
60.42% (G:22.17% B:3.84%) | Conf.: ± 0.003 (-0.212...-0.205) - [0.0%]
Duration: 48 minutes 36 seconds |
|
| 6. | Rollout1 | 21/10 | eq: -0.212 (-0.026) |
| Player:
Opponent: | 39.42% (G:12.65% B:1.28%)
60.58% (G:20.08% B:3.42%) | Conf.: ± 0.003 (-0.215...-0.209) - [0.0%]
Duration: 44 minutes 04 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 19183677
Moves: 3-ply, cube decisions: XG Roller
|
Gammon Save
| | White is Player 2
score: 0
pip: 158 | 2 point match
Crawford | pip: 171
score: 1
Blue is Player 1 |
|
| XGID=--Baa-C-B-ACda---c-bcAAAA-:0:0:1:65:1:0:1:2:10 |
| Blue to play 65 |
| 1. | Rollout1 | 21/10 | eq: -0.592 |
| Player:
Opponent: | 38.79% (G:14.29% B:1.88%)
61.21% (G:18.42% B:3.09%) | Conf.: ± 0.003 (-0.596...-0.589) - [100.0%]
Duration: 1 hour 30 minutes |
|
| 2. | Rollout1 | 24/18 23/18 | eq: -0.604 (-0.012) |
| Player:
Opponent: | 40.20% (G:13.15% B:1.68%)
59.80% (G:20.42% B:2.76%) | Conf.: ± 0.003 (-0.607...-0.601) - [0.0%]
Duration: 1 hour 37 minutes |
|
| 3. | Rollout1 | 22/16 21/16 | eq: -0.608 (-0.015) |
| Player:
Opponent: | 38.55% (G:11.62% B:1.31%)
61.45% (G:18.94% B:2.63%) | Conf.: ± 0.003 (-0.611...-0.605) - [0.0%]
Duration: 1 hour 31 minutes |
|
| 4. | Rollout1 | 11/5 10/5 | eq: -0.611 (-0.019) |
| Player:
Opponent: | 39.85% (G:16.78% B:2.20%)
60.15% (G:20.40% B:4.17%) | Conf.: ± 0.003 (-0.614...-0.608) - [0.0%]
Duration: 51 minutes 53 seconds |
|
| 5. | Rollout2 | 24/13* | eq: -0.631 (-0.038) |
| Player:
Opponent: | 39.69% (G:15.17% B:2.31%)
60.31% (G:21.23% B:4.54%) | Conf.: ± 0.006 (-0.637...-0.625) - [0.0%]
Duration: 51 minutes 06 seconds |
|
| 6. | Rollout3 | 10/4* 8/3* | eq: -0.696 (-0.103) |
| Player:
Opponent: | 39.52% (G:17.11% B:2.66%)
60.48% (G:24.31% B:6.58%) | Conf.: ± 0.006 (-0.702...-0.690) - [0.0%]
Duration: 25 minutes 01 second |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 70506927
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 70506927
Moves: 3-ply, cube decisions: XG Roller
3 5184 Games rolled with Variance Reduction.
Dice Seed: 17459709
Moves: 3-ply, cube decisions: XG Roller
|
Gammon Go
| | White is Player 2
score: 1
pip: 158 | 2 point match
Crawford | pip: 171
score: 0
Blue is Player 1 |
|
| XGID=--Baa-C-B-ACda---c-bcAAAA-:0:0:1:65:0:1:1:2:10 |
| Blue to play 65 |
| 1. | Rollout1 | 10/4* 8/3* | eq: +0.099 |
| Player:
Opponent: | 40.42% (G:14.55% B:1.75%)
59.58% (G:27.18% B:5.93%) | Conf.: ± 0.005 (+0.095...+0.104) - [100.0%]
Duration: 52 minutes 11 seconds |
|
| 2. | Rollout1 | 11/5 10/5 | eq: +0.075 (-0.025) |
| Player:
Opponent: | 40.90% (G:12.83% B:1.12%)
59.10% (G:21.12% B:3.85%) | Conf.: ± 0.004 (+0.070...+0.079) - [0.0%]
Duration: 40 minutes 13 seconds |
|
| 3. | Rollout1 | 24/13* | eq: +0.050 (-0.049) |
| Player:
Opponent: | 41.42% (G:11.09% B:1.36%)
58.58% (G:23.44% B:4.23%) | Conf.: ± 0.004 (+0.046...+0.055) - [0.0%]
Duration: 52 minutes 16 seconds |
|
| 4. | Rollout1 | 24/18 23/18 | eq: +0.036 (-0.064) |
| Player:
Opponent: | 41.27% (G:10.51% B:0.96%)
58.73% (G:23.13% B:3.53%) | Conf.: ± 0.004 (+0.031...+0.040) - [0.0%]
Duration: 47 minutes 05 seconds |
|
| 5. | Rollout1 | 21/10 | eq: +0.026 (-0.073) |
| Player:
Opponent: | 40.23% (G:11.08% B:0.79%)
59.77% (G:21.00% B:3.49%) | Conf.: ± 0.004 (+0.022...+0.030) - [0.0%]
Duration: 42 minutes 58 seconds |
|
| 6. | Rollout1 | 22/16 21/16 | eq: +0.019 (-0.081) |
| Player:
Opponent: | 39.97% (G:10.96% B:0.78%)
60.03% (G:23.24% B:4.10%) | Conf.: ± 0.004 (+0.014...+0.023) - [0.0%]
Duration: 47 minutes 11 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 52885855
Moves: 3-ply, cube decisions: XG Roller
|