1.  Rollout^{1}  Bar/23 6/2*  eq: 0.047 
 Player: Opponent:  43.61% (G:10.08% B:0.32%) 56.39% (G:18.44% B:0.56%)  Conf.: ± 0.010 (0.056...0.037)  [98.8%] Duration: 4 minutes 36 seconds 

2.  Rollout^{1}  Bar/23 8/4  eq: 0.065 (0.019) 
 Player: Opponent:  43.78% (G:11.51% B:0.38%) 56.22% (G:21.61% B:0.57%)  Conf.: ± 0.013 (0.079...0.052)  [1.2%] Duration: 4 minutes 16 seconds 

3.  Rollout^{1}  Bar/21 8/6  eq: 0.072 (0.025) 
 Player: Opponent:  43.55% (G:11.51% B:0.42%) 56.45% (G:22.19% B:0.53%)  Conf.: ± 0.011 (0.083...0.061)  [0.0%] Duration: 4 minutes 21 seconds 


^{1} 1296 Games rolled with Variance Reduction. Moves: 3ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10
1.  Rollout^{1}  Bar/21 8/6  eq: 0.292 
 Player: Opponent:  44.08% (G:11.65% B:0.38%) 55.92% (G:21.40% B:0.53%)  Conf.: ± 0.015 (0.307...0.277)  [98.2%] Duration: 41 minutes 17 seconds 

2.  Rollout^{1}  Bar/23 6/2*  eq: 0.316 (0.025) 
 Player: Opponent:  43.84% (G:10.23% B:0.32%) 56.16% (G:18.48% B:0.57%)  Conf.: ± 0.015 (0.331...0.301)  [1.1%] Duration: 45 minutes 18 seconds 

3.  Rollout^{1}  Bar/23 8/4  eq: 0.317 (0.026) 
 Player: Opponent:  43.84% (G:11.54% B:0.38%) 56.16% (G:21.11% B:0.53%)  Conf.: ± 0.014 (0.332...0.303)  [0.7%] Duration: 41 minutes 21 seconds 


^{1} 1296 Games rolled with Variance Reduction. Dice Seed: 29045956 Moves: 3ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10
The upper left diagram of this post shows the top three moves of Paul's original rollout result) of the position 52S43X53Z42@63R33O32T41P43151I42. To its right, in this post (you might have to widen your window so that my diagrams appear side by side), is the first 1k rollout result that I ran of the same position. Noting that different plays "won "(H in the first rollout, T in the second), I ran another 1k rollout—see lower left—and this time a third play (%) won. Aargh.
I did only those two 1k rollouts. Possibly, the #1, #2 and #3 results are all outliers, though the odds are against it. (At the same time, I'm sure that the H move would top the plurality, and probably the majority, of 1k rollouts.) I invite others to run their own experiments.
I then ran a much longer rollout, the result of which appears in the lower right.
Here is a nacbracs summary of the four independent rollout results:
........Rollout #1: ....[H .%19 .T25]. "<=1
........Rollout #2: ....[T .H25 .%26] ."<=1
........Rollout #3: ....[% .T12 .H24] ."<=1
........Long rollout: ....[H .%3 .T4] ."<=58
H = Hit (bar/23 6/2*), % = alt slot (bar/23 8/4), T = sTack/Tower (bar/21 8/6).
Nactation tutorial
Explanation of nacbracs
I hate to cramp anyone's style, as I realize there is a tradeoff of CPU time, but a lot of bgonliners see and learn from posted results. I'm only one voice, but I urge posters to extend middle game or (especially) early game rollouts to more than 1k trials. IMO, any move worth rolling out at all is worth rolling to at least 5k, even a weak move. If (say) a checker play that is reported to be an error of .03 is actually an error of .06, mentally assimilating the reported result throws off our intuitions, just as happens when (now and then) a play that is reported to be an error of .01 is actually best by .02.
Nack
1.  Rollout^{1}  Bar/23 8/4  eq: 0.299 
 Player: Opponent:  44.13% (G:11.45% B:0.39%) 55.87% (G:21.07% B:0.58%)  Conf.: ± 0.016 (0.315...0.283)  [85.9%] Duration: 14 minutes 56 seconds 

2.  Rollout^{1}  Bar/21 8/6  eq: 0.311 (0.012) 
 Player: Opponent:  43.96% (G:11.73% B:0.43%) 56.04% (G:21.34% B:0.53%)  Conf.: ± 0.013 (0.324...0.297)  [13.4%] Duration: 15 minutes 02 seconds 

3.  Rollout^{1}  Bar/23 6/2*  eq: 0.323 (0.024) 
 Player: Opponent:  43.81% (G:9.69% B:0.30%) 56.19% (G:18.28% B:0.50%)  Conf.: ± 0.014 (0.338...0.309)  [0.7%] Duration: 17 minutes 15 seconds 


^{1} 1296 Games rolled with Variance Reduction. Dice Seed: 81920408 Moves: 3ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10
1.  Rollout^{1}  Bar/23 6/2*  eq: 0.309 
 Player: Opponent:  43.89% (G:10.05% B:0.30%) 56.11% (G:18.36% B:0.55%)  Conf.: ± 0.002 (0.312...0.307)  [97.8%] Duration: 19 hours 01 minute 

2.  Rollout^{1}  Bar/23 8/4  eq: 0.313 (0.003) 
 Player: Opponent:  43.98% (G:11.48% B:0.38%) 56.02% (G:21.02% B:0.56%)  Conf.: ± 0.002 (0.315...0.311)  [1.7%] Duration: 16 hours 40 minutes 

3.  Rollout^{1}  Bar/21 8/6  eq: 0.314 (0.004) 
 Player: Opponent:  43.87% (G:11.61% B:0.42%) 56.13% (G:21.55% B:0.52%)  Conf.: ± 0.002 (0.316...0.312)  [0.4%] Duration: 16 hours 26 minutes 


^{1} 58000 Games rolled with Variance Reduction. Dice Seed: 33134295 Moves: 3ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10