With two checkers in the homeboard, the math simply how many roll bear both off for each of the 36 possible positions. It's binary - either you bear off both next roll or you don't.
If you consider positions where one of the checkers is outside the homeboard, then only doubles bear off in one roll and you may be choosing the position that makes it most likely to bear off in two rolls (or more if both are outside the homeboard). That's a much more difficult problem.
Alternatively, bearing in both checkers may be better than having a distance closest to e as the following counter-example shows. Here, a distance or 0 or 6 is better than a distance of 2 or 4.
     
 
      
 | | White is Player 2
score: 0
pip: 4 | | 1 point match | pip: 17
score: 0
Blue is Player 1 |
|
| XGID=--------AA--------------d-:0:0:1:32:0:0:0:1:10 |
| Blue to play 32 |
| 1. | Rollout1 | 8/3 | eq: -0.815 |
| Player:
Opponent: | 9.26% (G:0.00% B:0.00%)
90.74% (G:0.00% B:0.00%) | Conf.: ± 0.000 (-0.815...-0.815) - [100.0%]
Duration: 0.1 second |
|
| 2. | Rollout1 | 9/6 8/6 | eq: -0.815 |
| Player:
Opponent: | 9.26% (G:0.00% B:0.00%)
90.74% (G:0.00% B:0.00%) | Conf.: ± 0.000 (-0.815...-0.815) - [0.0%]
Duration: 0.6 second |
|
| 3. | Rollout1 | 9/7 8/5 | eq: -0.861 (-0.046) |
| Player:
Opponent: | 6.94% (G:0.00% B:0.00%)
93.06% (G:0.00% B:0.00%) | Conf.: ± 0.000 (-0.861...-0.861) - [0.0%]
Duration: 0.2 second |
|
| 4. | Rollout1 | 9/4 | eq: -0.861 (-0.046) |
| Player:
Opponent: | 6.94% (G:0.00% B:0.00%)
93.06% (G:0.00% B:0.00%) | Conf.: ± 0.000 (-0.861...-0.861) - [0.0%]
Duration: 0.1 second |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10, MET: Kazaross XG2