I discovered that if one adds a few more trials to the previously posted (25992-trial) file [@=P x0.2 H0.4], it is possible to get even closer on 4-ply, and to optionally put P (instead of @) on top. The three results below are with 26004, 26009 and 26010 trials, respectively:
[@=P x0.1 H0.4]
[@=P x0.2 H0.3]
[P=@ x0.2 H0.3]
Rollout details are below (followed by a couple of comments):
         
 
         
 | | White is Player 2
score: 0
pip: 146 | Unlimited Game
Jacoby Beaver | pip: 165
score: 0
Blue is Player 1 |
|
| XGID=-a----E-C-a-dE---b-dc-A-A-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 24/21 22/21 | eq: -0.4253 |
| Player:
Opponent: | 38.33% (G:6.30% B:0.19%)
61.67% (G:9.52% B:0.32%) | Conf.: ±0.0028 (-0.4281...-0.4224) - [25.3%]
Duration: 15 hours 52 minutes |
|
| 2. | Rollout1 | 8/5 6/5 | eq: -0.4253 (0.0000) |
| Player:
Opponent: | 40.21% (G:9.47% B:0.38%)
59.79% (G:18.36% B:0.71%) | Conf.: ±0.0033 (-0.4286...-0.4220) - [27.2%]
Duration: 13 hours 40 minutes |
|
| 3. | Rollout1 | 24/23 13/10* | eq: -0.4254 (-0.0001) |
| Player:
Opponent: | 40.66% (G:9.92% B:0.46%)
59.34% (G:20.32% B:0.97%) | Conf.: ±0.0035 (-0.4289...-0.4219) - [25.6%]
Duration: 14 hours 51 minutes |
|
| 4. | Rollout1 | 13/10* 10/9 | eq: -0.4256 (-0.0004) |
| Player:
Opponent: | 40.63% (G:10.33% B:0.47%)
59.37% (G:20.15% B:1.11%) | Conf.: ±0.0035 (-0.4292...-0.4221) - [21.8%]
Duration: 14 hours 41 minutes |
|
| |
1 26004 Games rolled with Variance Reduction.
Dice Seed: 88927773
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.01
| | White is Player 2
score: 0
pip: 146 | Unlimited Game
Jacoby Beaver | pip: 165
score: 0
Blue is Player 1 |
|
| XGID=-a----E-C-a-dE---b-dc-A-A-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 24/21 22/21 | eq: -0.4253 |
| Player:
Opponent: | 38.33% (G:6.30% B:0.19%)
61.67% (G:9.52% B:0.32%) | Conf.: ±0.0028 (-0.4281...-0.4225) - [25.2%]
Duration: 15 hours 52 minutes |
|
| 2. | Rollout1 | 8/5 6/5 | eq: -0.4253 |
| Player:
Opponent: | 40.21% (G:9.47% B:0.38%)
59.79% (G:18.36% B:0.71%) | Conf.: ±0.0033 (-0.4286...-0.4220) - [27.5%]
Duration: 13 hours 40 minutes |
|
| 3. | Rollout1 | 24/23 13/10* | eq: -0.4254 (-0.0002) |
| Player:
Opponent: | 40.65% (G:9.92% B:0.46%)
59.35% (G:20.32% B:0.97%) | Conf.: ±0.0035 (-0.4289...-0.4220) - [25.1%]
Duration: 14 hours 51 minutes |
|
| 4. | Rollout1 | 13/10* 10/9 | eq: -0.4256 (-0.0003) |
| Player:
Opponent: | 40.63% (G:10.33% B:0.47%)
59.37% (G:20.15% B:1.11%) | Conf.: ±0.0035 (-0.4291...-0.4221) - [22.2%]
Duration: 14 hours 41 minutes |
|
| |
1 26009 Games rolled with Variance Reduction.
Dice Seed: 88927773
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.01
| | White is Player 2
score: 0
pip: 146 | Unlimited Game
Jacoby Beaver | pip: 165
score: 0
Blue is Player 1 |
|
| XGID=-a----E-C-a-dE---b-dc-A-A-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 8/5 6/5 | eq: -0.4253 |
| Player:
Opponent: | 40.21% (G:9.47% B:0.38%)
59.79% (G:18.36% B:0.71%) | Conf.: ±0.0033 (-0.4286...-0.4220) - [28.1%]
Duration: 13 hours 40 minutes |
|
| 2. | Rollout1 | 24/21 22/21 | eq: -0.4253 (0.0000) |
| Player:
Opponent: | 38.33% (G:6.30% B:0.19%)
61.67% (G:9.52% B:0.32%) | Conf.: ±0.0028 (-0.4281...-0.4225) - [24.8%]
Duration: 15 hours 52 minutes |
|
| 3. | Rollout1 | 24/23 13/10* | eq: -0.4254 (-0.0002) |
| Player:
Opponent: | 40.65% (G:9.92% B:0.46%)
59.35% (G:20.32% B:0.97%) | Conf.: ±0.0035 (-0.4289...-0.4220) - [25.1%]
Duration: 14 hours 51 minutes |
|
| 4. | Rollout1 | 13/10* 10/9 | eq: -0.4256 (-0.0003) |
| Player:
Opponent: | 40.63% (G:10.33% B:0.47%)
59.37% (G:20.15% B:1.11%) | Conf.: ±0.0035 (-0.4291...-0.4221) - [22.1%]
Duration: 14 hours 41 minutes |
|
| |
1 26010 Games rolled with Variance Reduction.
Dice Seed: 88927773
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.01
Note that in the second of the three rollouts, the margin of the second play is blank. Does that mean that in the specific case the top two plays are so close that XG decided to make them look more similar by tainting neither play with .0000? :)
If I roll out the four plays a different number of trials, it is an easy matter to get all four plays within .0000 of each other. It is even possible that a seed exists at which all four plays are within .0000 with some same number of trials, but I'm not going to look for it. :)
Nack