1.  Rollout^{1}  6/4* 4/3  eq: +0.268 
 Player: Opponent:  56.08% (G:14.52% B:0.51%) 43.92% (G:8.43% B:0.33%)  Conf.: ± 0.003 (+0.265...+0.271)  [72.7%] Duration: 19 hours 51 minutes 

2.  Rollout^{1}  11/8  eq: +0.267 (0.001) 
 Player: Opponent:  56.60% (G:11.42% B:0.37%) 43.40% (G:6.80% B:0.24%)  Conf.: ± 0.002 (+0.264...+0.269)  [27.3%] Duration: 16 hours 30 minutes 

3.  Rollout^{2}  11/10 6/4*  eq: +0.252 (0.015) 
 Player: Opponent:  55.63% (G:14.47% B:0.52%) 44.37% (G:8.85% B:0.33%)  Conf.: ± 0.004 (+0.249...+0.256)  [0.0%] Duration: 8 hours 00 minute 

4.  Rollout^{3}  13/11 6/5  eq: +0.239 (0.029) 
 Player: Opponent:  55.65% (G:13.06% B:0.46%) 44.35% (G:8.10% B:0.31%)  Conf.: ± 0.005 (+0.234...+0.244)  [0.0%] Duration: 7 hours 32 minutes 


^{1} 41472 Games rolled with Variance Reduction. Dice Seed: 81920335 Moves: 3ply, cube decisions: XG Roller
^{2} 20736 Games rolled with Variance Reduction. Dice Seed: 81920335 Moves: 3ply, cube decisions: XG Roller
^{3} 10368 Games rolled with Variance Reduction. Dice Seed: 81920335 Moves: 3ply, cube decisions: XG Roller

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1.  Rollout^{1}  6/4* 4/3  eq: +0.270 
 Player: Opponent:  56.11% (G:14.46% B:0.52%) 43.89% (G:8.41% B:0.32%)  Conf.: ± 0.002 (+0.268...+0.272)  [99.9%] Duration: 11 hours 20 minutes 

2.  Rollout^{1}  11/8  eq: +0.266 (0.004) 
 Player: Opponent:  56.58% (G:11.44% B:0.37%) 43.42% (G:6.76% B:0.24%)  Conf.: ± 0.002 (+0.265...+0.268)  [0.1%] Duration: 9 hours 26 minutes 

3.  Rollout^{2}  11/10 6/4*  eq: +0.254 (0.017) 
 Player: Opponent:  55.66% (G:14.38% B:0.52%) 44.34% (G:8.82% B:0.34%)  Conf.: ± 0.003 (+0.251...+0.257)  [0.0%] Duration: 4 hours 28 minutes 

4.  Rollout^{3}  13/11 6/5  eq: +0.243 (0.028) 
 Player: Opponent:  55.66% (G:12.96% B:0.45%) 44.34% (G:8.05% B:0.31%)  Conf.: ± 0.004 (+0.238...+0.247)  [0.0%] Duration: 2 hours 11 minutes 


^{1} 82944 Games rolled with Variance Reduction. Moves: 3ply, cube decisions: XG Roller
^{2} 31104 Games rolled with Variance Reduction. Moves: 3ply, cube decisions: XG Roller
^{3} 15552 Games rolled with Variance Reduction. Moves: 3ply, cube decisions: XG Roller

1.  Rollout^{1}  11/10 6/4*  eq: +0.290 
 Player: Opponent:  56.34% (G:15.95% B:0.58%) 43.66% (G:9.20% B:0.34%)  Conf.: ± 0.006 (+0.284...+0.297)  [100.0%] Duration: 23 hours 24 minutes 

2.  Rollout^{1}  6/4* 4/3  eq: +0.265 (0.026) 
 Player: Opponent:  55.84% (G:14.98% B:0.53%) 44.16% (G:8.66% B:0.34%)  Conf.: ± 0.007 (+0.258...+0.271)  [0.0%] Duration: 1 day 00 hour 10 minutes 

3.  Rollout^{1}  11/8  eq: +0.251 (0.040) 
 Player: Opponent:  56.05% (G:11.89% B:0.39%) 43.95% (G:7.40% B:0.26%)  Conf.: ± 0.005 (+0.245...+0.256)  [0.0%] Duration: 20 hours 51 minutes 

4.  Rollout^{1}  13/11 6/5  eq: +0.240 (0.050) 
 Player: Opponent:  55.55% (G:13.40% B:0.45%) 44.45% (G:8.21% B:0.31%)  Conf.: ± 0.006 (+0.235...+0.246)  [0.0%] Duration: 1 day 00 hour 18 minutes 


^{1} 5184 Games rolled with Variance Reduction. Dice Seed: 33134270 Moves and cube decisions: 4ply Search interval: Large

The position shown twice above in the left column (rollout of 41k by me, then of 82k by Paul and Mike) was posed here (the sixth roll move from the sequence captioned here). The naturallooking "H" (Hit, 11/10 6/4*) is only third best, according to the rollouts.
The variant position on the right, which differs by only 1 pip, represents a situation we are more used to seeing, with White's trailing checker on the 24pt. In this (more common) position, H is clearly best. [If the 82k rollout and the 5k variant rollout do not appear sidebyside, either widen your window or imagine it.]
Here is a nacbracs summary of the data:
........64R42XF54Z41V21 .[3 L3 H16 $28 h85 D86] "<124*51 25 5
........64R42XF54Z31U31 .[H 326 L40 $50] "^5
The H/L swing is .053, and the H/3 swing is .042. Why is the "normal" H move downgraded to such an extent (to subpar) on the left?
For a complete explanation, one would need to examine and compare how all of White's rolls play in each position, which I haven't done. However, keeping in mind that Blue's advantage is smaller against White's 23pt checker than against her 24pt checker, here are a couple of key observations:
 The value of "L" (Lift, 11/8) is relatively enhanced on the left (against the 23pt checker) because there will be 5 fewer numbers that anchor or run to the midpoint on the left than on the right.
 The value of "3" (3pt, 6/4*/3  the oddlooking aceslide), is relatively enhanced on the left because it will saddle White with a bad 54. Perhaps a more elegant way to look at it is that leaving a 3pt blot will duplicate 53 on the left, while leaving a 4pt blot will duplicate 54 on the right.
Below, I've listed the candidate moves rolled out. Traditional notation is on the left, and Nactation (my choice, followed by alternatives) is on the right:
........11/10 6/4* ........H (Hit), N (Near), 0 (10pt), 4 (4pt)
........6/4*/3 ...............3 (3pt), i (inside)
........11/8 ..................L (Lift), T (sTack/Tower), 8 (8pt), D (Down)
........13/11 6/5 ..........$ (Slot), 1 (11pt), N (Near)
........13/11 8/7 ..........D (Down), % (alt slot)
........8/7 6/4* ............h (hit), n (near)
For further study, see the variant (of the above left position) diagrammed below, where one of Blue's 6pt spares is moved back to the midpoint. It is even less likely to arise (because one of Blue's checkers has to recycle) but is a useful reference position because four (almost five) moves are tied.
Nack
Nactation tutorial
Explanation of nacbracs
1.  Rollout^{1}  11/8  eq: +0.198 
 Player: Opponent:  54.87% (G:10.15% B:0.35%) 45.13% (G:6.95% B:0.24%)  Conf.: ± 0.002 (+0.195...+0.200)  [78.5%] Duration: 18 hours 41 minutes 

2.  Rollout^{1}  13/11 6/5  eq: +0.196 (0.001) 
 Player: Opponent:  54.85% (G:11.95% B:0.44%) 45.15% (G:8.99% B:0.33%)  Conf.: ± 0.003 (+0.193...+0.199)  [21.3%] Duration: 22 hours 26 minutes 

3.  Rollout^{1}  6/4* 4/3  eq: +0.193 (0.005) 
 Player: Opponent:  54.46% (G:13.22% B:0.48%) 45.54% (G:9.41% B:0.36%)  Conf.: ± 0.003 (+0.190...+0.195)  [0.2%] Duration: 22 hours 11 minutes 

4.  Rollout^{1}  11/10 6/4*  eq: +0.191 (0.007) 
 Player: Opponent:  54.42% (G:13.25% B:0.48%) 45.58% (G:9.62% B:0.36%)  Conf.: ± 0.003 (+0.188...+0.194)  [0.0%] Duration: 23 hours 11 minutes 

5.  Rollout^{2}  13/11 8/7  eq: +0.184 (0.013) 
 Player: Opponent:  54.11% (G:13.05% B:0.48%) 45.89% (G:8.90% B:0.33%)  Conf.: ± 0.004 (+0.180...+0.188)  [0.0%] Duration: 10 hours 30 minutes 

6.  Rollout^{3}  8/7 6/4*  eq: +0.137 (0.060) 
 Player: Opponent:  53.19% (G:13.14% B:0.49%) 46.81% (G:10.70% B:0.39%)  Conf.: ± 0.009 (+0.129...+0.146)  [0.0%] Duration: 3 hours 21 minutes 


^{1} 41472 Games rolled with Variance Reduction. Dice Seed: 29045956 Moves: 3ply, cube decisions: XG Roller
^{2} 20736 Games rolled with Variance Reduction. Dice Seed: 29045956 Moves: 3ply, cube decisions: XG Roller
^{3} 5184 Games rolled with Variance Reduction. Dice Seed: 29045956 Moves: 3ply, cube decisions: XG Roller

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