The position introduced here and repeated above is now verified as an R4 -- real four-score position. This means that there is a different best play at each of the four main scores (money, DMP, gammon save and gammon go), and each is clearly best -- it is not "tied" with any play that is best at any of the other three scores.
This position is the first R4 (found to date) for which the roll is a NON-doublet. The position can arise with perfect play as early as the 11th roll of the game (as captioned), and its power "score" is 19.21. Other R4's (along with detailed definitions of R4's and T4's, the definition of "tied," power scores, etc.) can be viewed here.
Future rollouts with stronger settings (or tedious manual audits of subsequent plays for adjustment of current rollouts) will no doubt increase or decrease the relative equity of some four-score plays, which in rare instances could downgrade play statuses (from R to T, or from T to not best). For example, as Tim observes for the position at hand, the blots in White's board might confuse XG to misplay next turn (hit and cover when it shouldn't, or not hit and cover when it should), though I think the odds are well against an overturn, given that lengthy 3-ply and 4-ply results seem to agree.
In the table below are nacbracs for each of the four scores -- m, d, s, g (money, DMP, gammon save and gammon go, respectively), for evaluations, 3-ply rollouts and 4-ply rollouts.
......XGR++ evaluation...............3-ply (XGR cube) rollout.............4-ply rollout
..m[J C23 R25 D34 O59]e.....m[J R12 C30 D38 O63] 62*5.....m[J R17] 10
...d[R J1 C4 D18 O36]e..........d[R J7 C15 D16 O36] 20*5........d[R J7] 10
...s[D O37 R65 J77]e...............s[D O43 R76 J90] 5
...
g[C J19 c59 Z73]e................g[C J11 c50 Z75] 15*5................g[C J10] 9
Key: C = Cross (20/15 8/5), c = cross (20/17 8/3), D = Down (13/10 13/8), J = Jump (8/5 8/3), O = Outer (13/5), R = Run (20/17 20/15), Z = reverse split (20/17 13/8).
Nactation tutorial • explanation of nacbracs
Detailed rollouts follow (scroll down).
Nack
m (Money), 3-ply rollout
           
 
         
 | | White is Player 2
score: 0
pip: 117 | Unlimited Game
Jacoby Beaver | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:0:3:0:10 |
| Blue to play 53 |
| 1. | Rollout1 | 8/5 8/3 | eq: +0.056 |
| Player:
Opponent: | 51.71% (G:11.73% B:0.35%)
48.29% (G:9.14% B:0.18%) | Conf.: ± 0.002 (+0.055...+0.058) - [100.0%]
Duration: 6 hours 31 minutes |
|
| 2. | Rollout1 | 20/17 20/15 | eq: +0.044 (-0.012) |
| Player:
Opponent: | 52.00% (G:6.60% B:0.30%)
48.00% (G:5.60% B:0.09%) | Conf.: ± 0.001 (+0.042...+0.045) - [0.0%]
Duration: 7 hours 37 minutes |
|
| 3. | Rollout2 | 20/15 8/5 | eq: +0.026 (-0.030) |
| Player:
Opponent: | 51.38% (G:14.46% B:0.50%)
48.62% (G:13.08% B:0.35%) | Conf.: ± 0.005 (+0.021...+0.031) - [0.0%]
Duration: 37 minutes 01 second |
|
| 4. | Rollout2 | 13/10 13/8 | eq: +0.018 (-0.038) |
| Player:
Opponent: | 51.31% (G:7.07% B:0.19%)
48.69% (G:3.59% B:0.09%) | Conf.: ± 0.005 (+0.013...+0.023) - [0.0%]
Duration: 51 minutes 35 seconds |
|
| 5. | Rollout2 | 13/5 | eq: -0.007 (-0.063) |
| Player:
Opponent: | 50.33% (G:10.14% B:0.33%)
49.67% (G:4.51% B:0.11%) | Conf.: ± 0.005 (-0.012...-0.002) - [0.0%]
Duration: 47 minutes 42 seconds |
|
| |
1 62208 Games rolled with Variance Reduction.
Dice Seed: 85897304
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 85897304
Moves: 3-ply, cube decisions: XG Roller
|
m (Money), 4-ply rollout
| | White is Player 2
score: 0
pip: 117 | Unlimited Game
Jacoby Beaver | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:0:3:0:10 |
| Blue to play 53 |
| 1. | Rollout1 | 8/5 8/3 | eq: +0.058 |
| Player:
Opponent: | 51.75% (G:12.03% B:0.37%)
48.25% (G:9.10% B:0.18%) | Conf.: ± 0.003 (+0.055...+0.061) - [100.0%]
Duration: 15 hours 13 minutes |
|
| 2. | Rollout1 | 20/17 20/15 | eq: +0.042 (-0.017) |
| Player:
Opponent: | 51.96% (G:6.40% B:0.30%)
48.04% (G:5.41% B:0.08%) | Conf.: ± 0.003 (+0.039...+0.045) - [0.0%]
Duration: 1 day 00 hour 07 minutes |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 85897304
Moves and cube decisions: 4-ply
Search interval: Large
|
d (DMP), 3-ply rollout
| | White is Player 2
score: 0
pip: 117 | | 1 point match | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:0:0:1:10 |
| Blue to play 53 |
| 1. | Rollout1 | 20/17 20/15 | eq: +0.036 |
| Player:
Opponent: | 51.81% (G:5.59% B:0.44%)
48.19% (G:4.43% B:0.07%) | Conf.: ± 0.001 (+0.035...+0.037) - [100.0%]
Duration: 3 hours 25 minutes |
|
| 2. | Rollout1 | 8/5 8/3 | eq: +0.029 (-0.007) |
| Player:
Opponent: | 51.45% (G:10.98% B:0.54%)
48.55% (G:7.94% B:0.12%) | Conf.: ± 0.001 (+0.028...+0.030) - [0.0%]
Duration: 2 hours 52 minutes |
|
| 3. | Rollout2 | 20/15 8/5 | eq: +0.021 (-0.015) |
| Player:
Opponent: | 51.07% (G:11.76% B:0.64%)
48.93% (G:11.08% B:0.22%) | Conf.: ± 0.002 (+0.020...+0.023) - [0.0%]
Duration: 28 minutes 23 seconds |
|
| 4. | Rollout2 | 13/10 13/8 | eq: +0.020 (-0.016) |
| Player:
Opponent: | 50.98% (G:6.64% B:0.37%)
49.02% (G:3.44% B:0.04%) | Conf.: ± 0.002 (+0.018...+0.021) - [0.0%]
Duration: 30 minutes 19 seconds |
|
| 5. | Rollout2 | 13/5 | eq: 0.000 (-0.036) |
| Player:
Opponent: | 49.99% (G:9.87% B:0.47%)
50.01% (G:5.47% B:0.12%) | Conf.: ± 0.002 (-0.002...+0.002) - [0.0%]
Duration: 28 minutes 01 second |
|
| |
1 20736 Games rolled with Variance Reduction.
Dice Seed: 58786193
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 58786193
Moves: 3-ply, cube decisions: XG Roller
|
d (DMP), 4-ply rollout
| | White is Player 2
score: 0
pip: 117 | | 1 point match | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:0:0:1:10 |
| Blue to play 53 |
| 1. | Rollout1 | 20/17 20/15 | eq: +0.037 |
| Player:
Opponent: | 51.84% (G:5.93% B:0.41%)
48.16% (G:4.57% B:0.06%) | Conf.: ± 0.001 (+0.036...+0.038) - [100.0%]
Duration: 1 day 08 hours 21 minutes |
|
| 2. | Rollout1 | 8/5 8/3 | eq: +0.030 (-0.007) |
| Player:
Opponent: | 51.52% (G:11.35% B:0.47%)
48.48% (G:8.08% B:0.11%) | Conf.: ± 0.001 (+0.029...+0.031) - [0.0%]
Duration: 23 hours 49 minutes |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 56025780
Moves and cube decisions: 4-ply
Search interval: Large
|
s (gammon save), 3-ply rollout
| | White is Player 2
score: 0
pip: 117 | 2 point match
Crawford | pip: 121
score: 1
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:1:0:1:2:10 |
| Blue to play 53 |
| 1. | Rollout1 | 13/10 13/8 | eq: -0.042 |
| Player:
Opponent: | 51.38% (G:7.13% B:0.38%)
48.62% (G:3.49% B:0.14%) | Conf.: ± 0.002 (-0.044...-0.040) - [100.0%]
Duration: 35 minutes 13 seconds |
|
| 2. | Rollout1 | 13/5 | eq: -0.086 (-0.043) |
| Player:
Opponent: | 50.05% (G:9.67% B:0.55%)
49.95% (G:4.33% B:0.16%) | Conf.: ± 0.002 (-0.088...-0.084) - [0.0%]
Duration: 33 minutes 56 seconds |
|
| 3. | Rollout1 | 20/17 20/15 | eq: -0.118 (-0.076) |
| Player:
Opponent: | 54.18% (G:13.45% B:1.45%)
45.82% (G:10.08% B:0.41%) | Conf.: ± 0.002 (-0.120...-0.115) - [0.0%]
Duration: 39 minutes 31 seconds |
|
| 4. | Rollout1 | 8/5 8/3 | eq: -0.132 (-0.090) |
| Player:
Opponent: | 50.84% (G:11.28% B:0.65%)
49.16% (G:7.46% B:0.26%) | Conf.: ± 0.002 (-0.135...-0.130) - [0.0%]
Duration: 31 minutes 41 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 56025780
Moves: 3-ply, cube decisions: XG Roller
|
g (gammon go), 3-ply rollout
| | White is Player 2
score: 1
pip: 117 | 2 point match
Crawford | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:1:1:2:10 |
| Blue to play 53 |
| 1. | Rollout1 | 20/15 8/5 | eq: +0.268 |
| Player:
Opponent: | 51.68% (G:11.73% B:0.46%)
48.32% (G:9.30% B:0.20%) | Conf.: ± 0.002 (+0.267...+0.270) - [100.0%]
Duration: 1 hour 44 minutes |
|
| 2. | Rollout1 | 8/5 8/3 | eq: +0.257 (-0.011) |
| Player:
Opponent: | 51.98% (G:10.86% B:0.38%)
48.02% (G:7.61% B:0.14%) | Conf.: ± 0.002 (+0.255...+0.258) - [0.0%]
Duration: 1 hour 38 minutes |
|
| 3. | Rollout2 | 20/17 8/3 | eq: +0.218 (-0.050) |
| Player:
Opponent: | 50.02% (G:10.88% B:0.35%)
49.98% (G:10.17% B:0.20%) | Conf.: ± 0.003 (+0.215...+0.221) - [0.0%]
Duration: 30 minutes 59 seconds |
|
| 4. | Rollout2 | 20/17 13/8 | eq: +0.193 (-0.075) |
| Player:
Opponent: | 49.90% (G:9.77% B:0.36%)
50.10% (G:9.35% B:0.22%) | Conf.: ± 0.003 (+0.191...+0.196) - [0.0%]
Duration: 33 minutes 03 seconds |
|
| |
1 15552 Games rolled with Variance Reduction.
Dice Seed: 56025780
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 56025780
Moves: 3-ply, cube decisions: XG Roller
|
g (gammon go), 4-ply rollout
| | White is Player 2
score: 1
pip: 117 | 2 point match
Crawford | pip: 121
score: 0
Blue is Player 1 |
|
| XGID=---CBBBbB---bB----beBb-aa-:0:0:1:53:0:1:1:2:10 |
| Blue to play 53 |
| 1. | Rollout1 | 20/15 8/5 | eq: +0.266 |
| Player:
Opponent: | 51.49% (G:11.82% B:0.48%)
48.51% (G:9.65% B:0.23%) | Conf.: ± 0.001 (+0.265...+0.268) - [100.0%]
Duration: 22 hours 12 minutes |
|
| 2. | Rollout1 | 8/5 8/3 | eq: +0.256 (-0.010) |
| Player:
Opponent: | 51.75% (G:11.04% B:0.40%)
48.25% (G:7.98% B:0.11%) | Conf.: ± 0.001 (+0.254...+0.257) - [0.0%]
Duration: 21 hours 30 minutes |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 85897304
Moves and cube decisions: 4-ply
Search interval: Large
|