I base my logic mostly on the sequence 51S-31P-51 rolled by David Rockwell (see below). I see two candidate plays here: 24/18; and 23/22, 13/8.
For the 51S-31P-51, 24/18, edges 23/22, 13/8 by a small margin. When adding 1.5 checkers in the zone (a spare on the 8 and the checker on the 11), I think the more conservative split should be best.
Therefore, 23/22, 13/8 is my play.
          
 
        
 | | White is Player 2
score: 0
pip: 163 | Unlimited Game
Jacoby Beaver | pip: 161
score: 0
Blue is Player 1 |
|
| XGID=-b----E-D---eD---b-db--AA-:0:0:1:51:0:0:3:0:10 |
| Blue to play 51 |
| 1. | Rollout1 | 24/18 | eq: -0.329 |
| Player:
Opponent: | 43.08% (G:10.77% B:0.56%)
56.92% (G:19.78% B:0.71%) | Conf.: ± 0.003 (-0.333...-0.326) - [95.4%]
Duration: 6 hours 47 minutes |
|
| 2. | Rollout1 | 23/22 13/8 | eq: -0.333 (-0.004) |
| Player:
Opponent: | 42.45% (G:11.43% B:0.59%)
57.55% (G:18.39% B:0.73%) | Conf.: ± 0.003 (-0.337...-0.330) - [4.6%]
Duration: 6 hours 51 minutes |
|
| 3. | XG Roller++ | 23/18 8/7 | eq: -0.374 (-0.044) |
| Player:
Opponent: | 41.83% (G:9.60% B:0.42%)
58.17% (G:19.03% B:0.96%) | |
|
| 4. | XG Roller++ | 13/8 6/5 | eq: -0.383 (-0.053) |
| Player:
Opponent: | 41.64% (G:10.59% B:0.49%)
58.36% (G:19.34% B:0.94%) | |
|
| 5. | XG Roller++ | 24/23 13/8 | eq: -0.410 (-0.081) |
| Player:
Opponent: | 40.09% (G:10.50% B:0.46%)
59.91% (G:18.01% B:0.78%) | |
|
| |
1 31104 Games rolled with Variance Reduction.
Dice Seed: 60902989
Moves: 3-ply, cube decisions: XG Roller
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eXtreme Gammon Version: 2.10