1.  Rollout^{1}  8/7* 8/3*  eq: +0.444 
 Player: Opponent:  58.68% (G:25.98% B:2.01%) 41.32% (G:12.27% B:0.92%)  Conf.: ± 0.004 (+0.439...+0.448)  [100.0%] Duration: 7 hours 35 minutes 

2.  Rollout^{1}  24/18  eq: +0.432 (0.012) 
 Player: Opponent:  60.41% (G:17.34% B:0.62%) 39.59% (G:8.04% B:0.32%)  Conf.: ± 0.004 (+0.428...+0.436)  [0.0%] Duration: 9 hours 54 minutes 

3.  Rollout^{1}  8/7* 6/1*  eq: +0.426 (0.017) 
 Player: Opponent:  58.30% (G:24.90% B:1.12%) 41.70% (G:11.75% B:0.72%)  Conf.: ± 0.005 (+0.422...+0.431)  [0.0%] Duration: 8 hours 49 minutes 

4.  Rollout^{2}  18/13 8/7*  eq: +0.404 (0.040) 
 Player: Opponent:  58.52% (G:21.11% B:1.23%) 41.48% (G:10.38% B:0.49%)  Conf.: ± 0.008 (+0.395...+0.412)  [0.0%] Duration: 1 hour 26 minutes 

5.  Rollout^{2}  10/5 6/5  eq: +0.395 (0.049) 
 Player: Opponent:  58.78% (G:22.10% B:1.26%) 41.22% (G:10.80% B:0.61%)  Conf.: ± 0.008 (+0.386...+0.403)  [0.0%] Duration: 1 hour 23 minutes 

6.  Rollout^{2}  24/23 18/13  eq: +0.393 (0.051) 
 Player: Opponent:  59.15% (G:18.53% B:0.86%) 40.85% (G:9.37% B:0.32%)  Conf.: ± 0.009 (+0.384...+0.402)  [0.0%] Duration: 1 hour 30 minutes 


^{1} 20736 Games rolled with Variance Reduction. Dice Seed: 43733867 Moves: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction. Dice Seed: 43733867 Moves: 3ply, cube decisions: XG Roller

According to the rollout, K (Kill, 8/7 8/3*) is best, @ (anchor, 24/18) is second, and lowercase k (kill, 8/7 6/1*) comes in third, but all three are very close. Six of seven respondents chose one of those top moves (two for K, three for @, and one for k).
Comparing the two doublehitters to each other, the move that breaks a point while keeping a fourstack and leaving an extra blot beats out (by .017) the safer move with the better distribution. This gives us an idea of the elevated importance of attacking on the higher inside point when hitting a second checker. When you're missed (which happens more often when you hit two checkers rather than one), securing the 3pt will be better than securing the 1pt, especially if the opponent immediately anchors on the other point.
Tim (who chose K), said, "There's probably a reason that Nack put a dilly builder on White's 4pt (duplicating White's threes everywhere?) but I'm missing the point of that hint." Indeed, one of my subgoals was to have 10/5 6/5 (making the 5pt) close enough that someone might vote for it. One respondent did take the bait, but only because he was sharp enough to notice the resulting duplication of 3s and 4s and 6s (not mentioned by anyone else).
I guess it was worth it, but I paid a price. Retrofitting a (wellplayed) game sequence was tricky with White having ten checkers behind her 8pt (and none on it), a stripped 6pt, a dilly on her 4pt, and three back checker blots laid bare with the other side on roll. Robert understandably asks how such a weird position could have arisen, and in how few moves with reasonable play. [Answer: With all moves being best or within .02, my solution requires 31 plays, with 51 being the 32nd roll.]
Near the end of the game sequence (spelled out beneath the diagram), each player has an opportunity to make an initial double. (In both cases, rollouts conclude that doubling is correct by less than .01, so not doubling is still well within the .02 threshold of "well played"). White's opportunity comes just prior to his second 41K, and Blue's opportunity comes just prior to his rolling the 51 that is on the board.
As the game sequence allows for this flexibility, I have included two additional rollouts below (which can be viewed sidebyside if you widen your window): one with Blue owning the cube, and one with White owning the cube.
Immediately below are the nacbracs summaries (also shown in the captions) for playing 51 with the three different positionings of the cube. I'll let you derive your own conclusions or speculations.
........Cube in center.... [K @12 k17 X40 P49 R51] "<=20**5
........Blue owns cube.. [K k17 @23 P33 X42 R42] "<=10**5
........White owns cube [@ K13 k21 P27 R35 X40] "<=10**5
Key: K = Kill (8/7* 8/3), k = kill 8/7* 6/1*, @ = anchor (24/18), X = hit and split (18/13 8/7*), P = Point (10/5 6/5), R = Run (24/23 18/13).
........Nactation tutorial ....(For larger text, click on the doublearrow to the right of “Bookmarks”)
........Explanation of nacbracs
Nack
1.  Rollout^{1}  8/7* 8/3*  eq: +0.554 
 Player: Opponent:  58.51% (G:26.38% B:1.97%) 41.49% (G:12.51% B:0.99%)  Conf.: ± 0.005 (+0.549...+0.559)  [100.0%] Duration: 2 hours 46 minutes 

2.  Rollout^{1}  8/7* 6/1*  eq: +0.537 (0.017) 
 Player: Opponent:  58.32% (G:24.90% B:1.13%) 41.68% (G:11.77% B:0.73%)  Conf.: ± 0.005 (+0.532...+0.542)  [0.0%] Duration: 2 hours 46 minutes 

3.  Rollout^{1}  24/18  eq: +0.531 (0.023) 
 Player: Opponent:  60.39% (G:17.53% B:0.65%) 39.61% (G:8.04% B:0.32%)  Conf.: ± 0.005 (+0.527...+0.536)  [0.0%] Duration: 2 hours 58 minutes 

4.  Rollout^{2}  10/5 6/5  eq: +0.520 (0.033) 
 Player: Opponent:  58.67% (G:22.29% B:1.31%) 41.33% (G:10.85% B:0.60%)  Conf.: ± 0.006 (+0.514...+0.527)  [0.0%] Duration: 1 hour 39 minutes 

5.  Rollout^{2}  18/13 8/7*  eq: +0.512 (0.042) 
 Player: Opponent:  58.37% (G:21.21% B:1.28%) 41.63% (G:10.42% B:0.49%)  Conf.: ± 0.007 (+0.505...+0.519)  [0.0%] Duration: 1 hour 36 minutes 

6.  Rollout^{2}  24/23 18/13  eq: +0.512 (0.042) 
 Player: Opponent:  59.18% (G:18.87% B:0.89%) 40.82% (G:9.45% B:0.35%)  Conf.: ± 0.007 (+0.505...+0.519)  [0.0%] Duration: 1 hour 48 minutes 


^{1} 10368 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3ply, cube decisions: XG Roller

1.  Rollout^{1}  24/18  eq: +0.162 
 Player: Opponent:  60.43% (G:17.63% B:0.66%) 39.57% (G:8.02% B:0.32%)  Conf.: ± 0.004 (+0.158...+0.166)  [100.0%] Duration: 3 hours 07 minutes 

2.  Rollout^{1}  8/7* 8/3*  eq: +0.149 (0.013) 
 Player: Opponent:  58.52% (G:26.42% B:2.01%) 41.48% (G:12.45% B:0.95%)  Conf.: ± 0.005 (+0.145...+0.154)  [0.0%] Duration: 3 hours 21 minutes 

3.  Rollout^{1}  8/7* 6/1*  eq: +0.141 (0.021) 
 Player: Opponent:  58.44% (G:25.00% B:1.12%) 41.56% (G:11.79% B:0.71%)  Conf.: ± 0.004 (+0.137...+0.145)  [0.0%] Duration: 4 hours 11 minutes 

4.  Rollout^{2}  10/5 6/5  eq: +0.135 (0.027) 
 Player: Opponent:  58.67% (G:21.90% B:1.23%) 41.33% (G:10.54% B:0.58%)  Conf.: ± 0.006 (+0.129...+0.140)  [0.0%] Duration: 2 hours 08 minutes 

5.  Rollout^{2}  24/23 18/13  eq: +0.127 (0.035) 
 Player: Opponent:  59.13% (G:19.07% B:0.91%) 40.87% (G:9.32% B:0.33%)  Conf.: ± 0.005 (+0.122...+0.132)  [0.0%] Duration: 2 hours 08 minutes 

6.  Rollout^{2}  18/13 8/7*  eq: +0.122 (0.040) 
 Player: Opponent:  58.41% (G:21.69% B:1.37%) 41.59% (G:10.44% B:0.47%)  Conf.: ± 0.006 (+0.117...+0.128)  [0.0%] Duration: 2 hours 27 minutes 


^{1} 10368 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3ply, cube decisions: XG Roller
