Stick got this one wrong over on rec.games.backgammon, but Bob Koca nailed it (although he mistakenly typed 21/19 7/6 instead of 21/20 8/6). White's priority is to save the gammon if possible. So if she rolls 21, then 8/6 7/6 is the right play.
        
 
       
 | | White is Player 2
score: 0
pip: 122 | Unlimited Game
Jacoby Beaver | pip: 20
score: 0
Blue is Player 1 |
|
| XGID=-CDCb------------bagc-----:1:-1:-1:12:0:0:3:0:10 |
| White to play 12 |
| 1. | Rollout1 | 8/6 7/6 | eq: -1.836 |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:83.56% B:0.02%) | Conf.: ± 0.000 (-1.836...-1.836) - [100.0%]
Duration: 5.8 seconds |
|
| 2. | Rollout1 | 21/20 8/6 | eq: -1.855 (-0.019) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:85.49% B:0.02%) | Conf.: ± 0.000 (-1.855...-1.855) - [0.0%]
Duration: 7.3 seconds |
|
| 3. | Rollout1 | 21/19 7/6 | eq: -1.859 (-0.023) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:85.85% B:0.00%) | Conf.: ± 0.000 (-1.859...-1.858) - [0.0%]
Duration: 8.4 seconds |
|
| 4. | Rollout1 | 8/6 5/4 | eq: -1.859 (-0.024) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:85.89% B:0.06%) | Conf.: ± 0.000 (-1.860...-1.859) - [0.0%]
Duration: 11.6 seconds |
|
| 5. | Rollout1 | 8/7 8/6 | eq: -1.865 (-0.029) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:86.47% B:0.01%) | Conf.: ± 0.000 (-1.865...-1.865) - [0.0%]
Duration: 9.2 seconds |
|
| 6. | Rollout1 | 21/18 | eq: -1.866 (-0.030) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:86.62% B:0.00%) | Conf.: ± 0.000 (-1.866...-1.866) - [0.0%]
Duration: 10.2 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 4-ply, cube decisions: XG Roller+
Search interval: Large
|
eXtreme Gammon Version: 2.19.211.pre-release
Even so, it looks as though White is still in no danger of losing a backgammon, since she is only 6 pips away from running off the backgammon, and will have at least two rolls to do so, even if Blue rolls repeated boxcars. But look at what happens if Blue takes two checkers off his 3pt and White rolls 21 again:
 
 
| | White is Player 2
score: 0
pip: 119 | Unlimited Game
Jacoby Beaver | pip: 14
score: 0
Blue is Player 1 |
|
| XGID=-CDAb------------a-ic-----:1:-1:-1:12:0:0:3:0:10 |
| White to play 12 |
| 1. | Rollout1 | 21/20 8/6 | eq: -1.9247 |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:91.90% B:0.57%) | Conf.: ±0.0001 (-1.9248...-1.9245) - [100.0%]
Duration: 24.2 seconds |
|
| 2. | Rollout1 | 21/18 | eq: -1.9255 (-0.0008) |
| Player:
Opponent: | 0.00% (G:0.00% B:0.00%)
100.00% (G:92.55% B:0.00%) | Conf.: ±0.0002 (-1.9257...-1.9254) - [0.0%]
Duration: 31.8 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic
|
eXtreme Gammon Version: 2.19.211.pre-release
The play of 21/20 8/6 saves enough extra gammons to justify the slight risk of losing a backgammon.