Thanks, Leo. I got around to doing a couple of rollouts myself.
The first position below is the same as yours except that I've changed the score to an unlimited game, to avoid peculiarities associated with the particular score such as the gammon values. Breaking anchor still comes out on top. The interesting thing is that the computer doubles as White after the anchor-breaking play but does not double after the board-breaking play; nevertheless the play that provokes the cube turn comes out ahead.
The second position below is the same as the first position but with Blue owning the cube. Now the two plays are essentially tied. In effect we are "forcing" White to double after either play.

              
 
              
 | | White is Player 2
score: 0 pip: 109 | Unlimited Game | pip: 100 score: 0
Blue is Player 1 | |
XGID=-ABCBbB-C--a------bccBb-b-:1:-1:1:65:0:0:0:0:10 |
Blue to play 65 |
1. | Rollout1 | 21/16 21/15 | eq: -0.599 |
| Player: Opponent: | 37.95% (G:6.89% B:0.26%) 62.05% (G:24.97% B:0.71%) | Conf.: ± 0.012 (-0.611...-0.587) - [100.0%] Duration: 13 minutes 53 seconds |
|
2. | Rollout2 | 8/2 6/1 | eq: -0.655 (-0.056) |
| Player: Opponent: | 35.27% (G:4.06% B:0.06%) 64.73% (G:14.99% B:0.49%) | Conf.: ± 0.008 (-0.664...-0.647) - [0.0%] Duration: 6 minutes 14 seconds |
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|
1 1296 Games rolled with Variance Reduction. Rolled for both No double and Double Dice Seed: 271828 First 3 moves: 3-ply, cube decisions: XG Roller+ Remaining moves: 3-ply, cube decisions: XG Roller
2 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.19.208.pre-release

              
 
              
 | | White is Player 2
score: 0 pip: 109 | Unlimited Game | pip: 100 score: 0
Blue is Player 1 | |
XGID=-ABCBbB-C--a------bccBb-b-:1:1:1:65:0:0:0:0:10 |
Blue to play 65 |
1. | Rollout1 | 8/2 6/1 | eq: -0.290 |
| Player: Opponent: | 34.75% (G:3.75% B:0.06%) 65.25% (G:14.38% B:0.45%) | Conf.: ± 0.006 (-0.297...-0.284) - [95.8%] Duration: 5 minutes 15 seconds |
|
2. | Rollout1 | 21/16 21/15 | eq: -0.298 (-0.007) |
| Player: Opponent: | 37.80% (G:6.93% B:0.27%) 62.20% (G:24.64% B:0.68%) | Conf.: ± 0.006 (-0.303...-0.292) - [4.2%] Duration: 5 minutes 14 seconds |
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|
1 1296 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.19.208.pre-release