The correct play is 13/8 13/7. Second best (my play over the board) is 13/2. Third is 13/7 6/1*. Correct cube action is Double/Take after all three plays.
Why is the 23-shot play (13/8 13/7) better than the 11-shot play (13/2)?
If you are not hit, you are much better off having the checkers on the 7pt and 8pt than one on the 2pt. If you are hit, 13/8 13/7 leaves you with a ninth checker in the zone, a spare on the 8pt. If you are hit after 13/2, you have only eight checkers in the zone.
There is also the matter of duplication. Black's aces (other than 11) are lousy. A lot of Black's 6s and 4s are good anyway. In particular, Black's 66 44 and 22 are jokers regardless of the play you make. Black's 64 and 42 are strong anchoring rolls. Black's 65 63 and 54 are strong running-to-safety rolls.
Summary: Playing 13/2 gives Black great aces, a lot of good 6s and 4s, a suboptimal position if missed, and a lousy position if hit.
Four rollouts are posted below.

              
                   
 | is shimohei
score: 0 pip: 149 | | 9 point match | pip: 150 score: 6
is peever | |
| XGID=-a-aB-D-B---cF---bbdb---A-:0:0:1:65:6:0:0:9:10 |
to play 65 |
| 1. | Rollout1 | 13/8 13/7 | eq: -0.765 |
| Player: Opponent: | 38.39% (G:10.46% B:1.40%) 61.61% (G:19.23% B:0.72%) | Conf: ± 0.023 (-0.788...-0.742) Duration: 14 minutes 44 seconds |
|
| 2. | Rollout1 | 13/2 | eq: -0.810 (-0.045) |
| Player: Opponent: | 38.47% (G:10.70% B:1.26%) 61.53% (G:21.41% B:0.61%) | Conf: ± 0.022 (-0.832...-0.788) Duration: 13 minutes 30 seconds |
|
| 3. | Rollout1 | 13/7 6/1* | eq: -0.839 (-0.075) |
| Player: Opponent: | 37.84% (G:10.98% B:0.89%) 62.16% (G:21.42% B:0.95%) | Conf: ± 0.022 (-0.861...-0.817) Duration: 15 minutes 32 seconds |
|
| |
1 1296 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.20, MET: Rockwell-Kazaross

              
                   
 | is shimohei
score: 0 pip: 149 | | 9 point match | pip: 139 score: 6
is peever | |
| XGID=-aAaB-D-B---cE---bbdb---A-:0:0:-1:00:6:0:0:9:10 |
on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.59% (G: 20.08% B: 0.61%) |
| Opponent Winning Chances: | 38.41% (G: 10.44% B: 1.15%) |
| Double/Take |
| Player Winning Chances: | 61.41% (G: 21.41% B: 0.54%) |
| Opponent Winning Chances: | 38.59% (G: 10.68% B: 1.47%) |
| |
| Cubeless Equities |
| No Double: | +0.309 |
| Double: | +0.828 |
| |
| Cubeful Equities |
| No Double: | +0.759 (-0.048) |
| Double/Take: | +0.808 |
| Double/Drop: | +1.000 (+0.192) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.018 (+0.741...+0.777) |
| Confidence Double: | ± 0.021 (+0.787...+0.829) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 45 minutes 28 seconds |
eXtreme Gammon Version: 1.20, MET: Rockwell-Kazaross

              
                   
 | is shimohei
score: 0 pip: 149 | | 9 point match | pip: 139 score: 6
is peever | |
| XGID=-a-aB-DAC---cD---bbdb---A-:0:0:-1:00:6:0:0:9:10 |
on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.56% (G: 18.68% B: 0.68%) |
| Opponent Winning Chances: | 38.44% (G: 10.39% B: 0.99%) |
| Double/Take |
| Player Winning Chances: | 61.89% (G: 19.22% B: 0.64%) |
| Opponent Winning Chances: | 38.11% (G: 10.58% B: 1.43%) |
| |
| Cubeless Equities |
| No Double: | +0.299 |
| Double: | +0.798 |
| |
| Cubeful Equities |
| No Double: | +0.696 (-0.074) |
| Double/Take: | +0.770 |
| Double/Drop: | +1.000 (+0.230) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.018 (+0.678...+0.714) |
| Confidence Double: | ± 0.022 (+0.748...+0.792) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 52 minutes 23 seconds |
eXtreme Gammon Version: 1.20, MET: Rockwell-Kazaross

              
                   
 | is shimohei
score: 0 pip: 150 | | 9 point match | pip: 139 score: 6
is peever | |
| XGID=aA-aB-CAB---cE---bbdb---A-:0:0:-1:00:6:0:0:9:10 |
on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 61.91% (G: 20.62% B: 0.91%) |
| Opponent Winning Chances: | 38.09% (G: 10.42% B: 0.76%) |
| Double/Take |
| Player Winning Chances: | 62.31% (G: 21.23% B: 0.84%) |
| Opponent Winning Chances: | 37.69% (G: 10.61% B: 1.27%) |
| |
| Cubeless Equities |
| No Double: | +0.328 |
| Double: | +0.868 |
| |
| Cubeful Equities |
| No Double: | +0.758 (-0.088) |
| Double/Take: | +0.846 |
| Double/Drop: | +1.000 (+0.154) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.018 (+0.740...+0.776) |
| Confidence Double: | ± 0.023 (+0.823...+0.869) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 53 minutes 58 seconds |
eXtreme Gammon Version: 1.20, MET: Rockwell-Kazaross