Studying this position after the fact, I've become convinced that strategically, hitting and jumping out is the right idea here. "Small" changes in the position (see below) make hitting and jumping out the winner by a country mile. Thus it's quite surprising to me that the computer judges that, in the original position, tactical considerations override the strategic imperatives.

              
 
              
 | | White is Player 2
score: 0 pip: 121 | Money session Jacoby | pip: 144 score: 0
Blue is Player 1 | |
| XGID=a-Ba-BCAC----A---bbeb-BbA-:0:0:1:63:0:0:1:0:10 |
| Blue to play 63 |
| 1. | Rollout1 | 24/15 | eq: +0.262 |
| Player: Opponent: | 56.24% (G:17.20% B:0.65%) 43.76% (G:14.60% B:0.80%) | Conf: ± 0.012 (+0.250...+0.274) Duration: 4 hours 38 minutes |
|
| 2. | Rollout1 | 22/16 6/3* | eq: +0.231 (-0.031) |
| Player: Opponent: | 55.52% (G:18.92% B:0.75%) 44.48% (G:20.33% B:2.80%) | Conf: ± 0.010 (+0.221...+0.241) Duration: 4 hours 02 minutes |
|
| 3. | Rollout1 | 13/7 6/3* | eq: +0.211 (-0.052) |
| Player: Opponent: | 54.87% (G:17.91% B:0.68%) 45.13% (G:15.17% B:0.81%) | Conf: ± 0.012 (+0.199...+0.223) Duration: 3 hours 49 minutes |
|
| 4. | Rollout1 | 24/21 13/7 | eq: +0.195 (-0.068) |
| Player: Opponent: | 54.16% (G:15.82% B:0.58%) 45.84% (G:12.28% B:0.49%) | Conf: ± 0.010 (+0.185...+0.205) Duration: 3 hours 49 minutes |
|
| |
1 5001 Games rolled with Variance Reduction. Dice Seed: 2 Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21

              
 
              
 | | White is Player 2
score: 0 pip: 121 | Money session Jacoby | pip: 142 score: 0
Blue is Player 1 | |
| XGID=a-Ba-BDAB----A---bbeb-BbA-:0:0:1:63:0:0:1:0:10 |
| Blue to play 63 |
| 1. | XG Roller+ | 22/16 6/3* | eq: +0.323 |
| Player: Opponent: | 57.03% (G:22.50% B:0.90%) 42.97% (G:19.82% B:3.33%) | |
|
| 2. | XG Roller+ | 13/7 6/3* | eq: +0.316 (-0.006) |
| Player: Opponent: | 56.93% (G:20.85% B:0.84%) 43.07% (G:14.65% B:0.91%) | |
|
| 3. | XG Roller+ | 24/15 | eq: +0.201 (-0.122) |
| Player: Opponent: | 54.57% (G:18.47% B:0.72%) 45.43% (G:14.73% B:0.80%) | |
|
| 4. | XG Roller+ | 24/21 13/7 | eq: +0.140 (-0.182) |
| Player: Opponent: | 53.13% (G:16.50% B:0.67%) 46.87% (G:13.10% B:0.54%) | |
|
eXtreme Gammon Version: 1.21

              
 
              
 | | White is Player 2
score: 0 pip: 120 | Money session Jacoby | pip: 144 score: 0
Blue is Player 1 | |
| XGID=a-B-aBCAC----A---bbeb-BbA-:0:0:1:63:0:0:1:0:10 |
| Blue to play 63 |
| 1. | XG Roller+ | 22/16 7/4* | eq: +0.272 |
| Player: Opponent: | 56.45% (G:21.47% B:0.90%) 43.55% (G:19.08% B:2.11%) | |
|
| 2. | XG Roller+ | 24/15 | eq: +0.187 (-0.085) |
| Player: Opponent: | 54.40% (G:17.39% B:0.70%) 45.60% (G:14.32% B:0.72%) | |
|
| 3. | XG Roller+ | 13/4* | eq: +0.180 (-0.092) |
| Player: Opponent: | 54.05% (G:20.23% B:0.81%) 45.95% (G:17.78% B:1.23%) | |
|
| 4. | XG Roller+ | 24/21 13/7 | eq: +0.113 (-0.159) |
| Player: Opponent: | 52.10% (G:16.34% B:0.66%) 47.90% (G:12.50% B:0.51%) | |
|
eXtreme Gammon Version: 1.21
Here's what it takes to make my play come out on top.

              
 
              
 | | White is Player 2
score: 0 pip: 123 | Money session Jacoby | pip: 144 score: 0
Blue is Player 1 | |
| XGID=aaB--BCAC----A---bbeb-BbA-:0:0:1:63:0:0:1:0:10 |
| Blue to play 63 |
| 1. | XG Roller+ | 24/21 13/7 | eq: +0.316 |
| Player: Opponent: | 58.08% (G:17.38% B:0.81%) 41.92% (G:11.22% B:0.42%) | |
|
| 2. | XG Roller+ | 24/15 | eq: +0.257 (-0.059) |
| Player: Opponent: | 56.64% (G:17.37% B:0.69%) 43.36% (G:13.76% B:0.64%) | |
|
eXtreme Gammon Version: 1.21