In the perfectly played game sequence above, the last two moves were Blue's 52 and White's 21. Now Blue rolls 11.
Respondents mentioned six moves (five of which garnered primary support). These moves (listed below, alphabetically) are indeed worthy of attention:
.....D (Down) = 13/8
.....E (Each) = 24/23 14/13 4/3*(2)
.....F (Field 2110) = 24/23 14/13 8/6
.....I (Inside) = 4/3*/2*(2)
.....y (Yosemite 1102) = 24/23 8/7 4/3*(2)
.....Y (Yosemite 1102) = 24/23 12/11 4/3*(2)
Let's start with Money (i.e., Unlimited with Jacoby and beavers). The best move, which is Y (Yosemite) = 24/23 12/11 4/3*(2), was chosen by four respondents. Joe Russell: "I am protected against the fly shots by the Jacoby Rule and want to build a counter-prime. Mike Clapsadle: "Anchor up in the back and be ready to come out. Put one of his checkers on the bar to keep him busy, and create another builder to make the 8pt." Casper: "You have also spoken for me, Mike!"
[Note Joe's observation about the Jacoby rule. At "normal" match scores, or if the cube is turned, the gammon save play is best. For anyone interested, the rollout results are +C[y E16 F26 Y29] "<=20*10, and –C[y Y14 E21 F35] "<=20**5 (where +C means Blue owns the cube, and –C means that White owns the cube). At "normal" match scores (cube unturned), 3-ply and 4-ply results are n[Y y5 F27 E31] "<=62*5 and [Y y2] "^20.]
At DMP, the best move is D (Down) = 12/8, which was chosen by three respondents (including Grudgen). Mike C: "Make the 8pt and 5pt prime to match your opponent. Looks like he will have to crack before you." And Casper: Ditto.
At gammon save, the best move is y (Yosemite) = 24/23 8/7 4/3*(2), which was chosen by Joe and Taper Mike. Joe said, "I am making the 23 point for sure. I would play 4-3(2) and for the final ace 8-7. 14-13 for the final ace is also reasonable. It would not surprise me much if 24-23, 14-13, 8-6 is best."
At gammon go, the best move is I (Inside) = 4/3*/2*(2), which was chosen by five respondents (including Grudgen). For Joe, "This seems like the easiest choice of the four states to me." And Mike C: "Put both of his on the bar. If you get a 6 in the next couple rolls, he should end up with 3, maybe 4 checkers back." Casper: Ditto. Finally, Taper Mike: "Anything could happen with two on the roof. Unfortunately, [this play] leaves a double gap that will be very difficult to fill with out undertaking risky attacking maneuvers. Probably, it is illadvised at most scores." (There are several other insightful comments in Mike's post.)
Below are nacbracs of the rollout results:
....................3-ply.........................................4-ply
.....m [Y y33 F55 E69...] "<=10*5............m [Y y29] "^5
......d [D Y11 E25 y26 F32...] "<=20*5.....d [D Y11] "^5
......s [y F8 Y23...] "<=62*15 5..................s [y F9] "^12
......g [I Y13 y15...] "<=15**5....................g [I Y13 y14] "^5
Key: D (Down) = 13/8, E (Each) = 24/23 14/13 4/3*(2), F (Field 2110) = 24/23 14/13 8/6, I (Inside) = 4/3*/2*(2), y (Yosemite 1102) = 24/23 8/7 4/3*(2), Y = 24/23 12/11 4/3*(2).
Nactation tutorial • explanation of nacbracs
In short, a different play is best -- in fact, clearly best (better than "tied," according to the B/W error scale) -- at each of the four main scores. Below are detailed rollout results.
Finally, there are (at least) two scores at which a fifth play is best! Extra credit to anyone who can find either of these scores -- feel free to consult XG evals and/or rollouts. The answer (plus much more) will be revealed in a separate post.
Nack
(m) Money 3-ply
| | White is Player 2
score: 0 pip: 119 | Unlimited Game Jacoby Beaver | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:0:3:0:10 |
Blue to play 11 |
1. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.152 |
| Player: Opponent: | 53.94% (G:14.45% B:0.93%) 46.06% (G:19.10% B:1.86%) | Conf.: ± 0.006 (+0.146...+0.157) - [100.0%] Duration: 2 hours 20 minutes |
|
2. | Rollout1 | 24/23 8/7 4/3*(2) | eq: +0.119 (-0.033) |
| Player: Opponent: | 53.10% (G:14.74% B:0.86%) 46.90% (G:16.44% B:1.14%) | Conf.: ± 0.005 (+0.114...+0.124) - [0.0%] Duration: 2 hours 32 minutes |
|
3. | Rollout2 | 24/23 14/13 8/6 | eq: +0.097 (-0.055) |
| Player: Opponent: | 52.53% (G:13.11% B:0.58%) 47.47% (G:15.78% B:0.87%) | Conf.: ± 0.007 (+0.089...+0.104) - [0.0%] Duration: 1 hour 43 minutes |
|
4. | Rollout2 | 24/23 14/13 4/3*(2) | eq: +0.083 (-0.069) |
| Player: Opponent: | 52.93% (G:13.93% B:0.83%) 47.07% (G:16.75% B:1.02%) | Conf.: ± 0.007 (+0.075...+0.090) - [0.0%] Duration: 1 hour 43 minutes |
|
5. | Rollout2 | 24/23 12/11(2) 8/7 | eq: +0.053 (-0.099) |
| Player: Opponent: | 52.34% (G:12.32% B:0.52%) 47.66% (G:18.11% B:1.18%) | Conf.: ± 0.007 (+0.046...+0.060) - [0.0%] Duration: 1 hour 34 minutes |
|
6. | Rollout2 | 24/23 8/5 | eq: +0.045 (-0.107) |
| Player: Opponent: | 52.21% (G:12.43% B:0.53%) 47.79% (G:18.20% B:1.15%) | Conf.: ± 0.008 (+0.036...+0.053) - [0.0%] Duration: 1 hour 26 minutes |
|
7. | Rollout2 | 24/23 13/12 8/6 | eq: +0.043 (-0.109) |
| Player: Opponent: | 51.27% (G:12.18% B:0.53%) 48.73% (G:16.34% B:0.89%) | Conf.: ± 0.008 (+0.035...+0.050) - [0.0%] Duration: 1 hour 32 minutes |
|
8. | Rollout2 | 4/3*(2) 3/2*(2) | eq: +0.041 (-0.111) |
| Player: Opponent: | 49.08% (G:20.72% B:1.80%) 50.92% (G:21.47% B:3.14%) | Conf.: ± 0.010 (+0.031...+0.050) - [0.0%] Duration: 1 hour 46 minutes |
|
9. | Rollout2 | 24/23 13/12 4/3*(2) | eq: +0.039 (-0.112) |
| Player: Opponent: | 51.55% (G:13.50% B:0.78%) 48.45% (G:17.79% B:1.17%) | Conf.: ± 0.007 (+0.032...+0.046) - [0.0%] Duration: 1 hour 29 minutes |
|
10. | Rollout2 | 12/8 | eq: -0.033 (-0.185) |
| Player: Opponent: | 54.11% (G:12.89% B:0.59%) 45.89% (G:25.63% B:2.73%) | Conf.: ± 0.009 (-0.042...-0.024) - [0.0%] Duration: 1 hour 34 minutes |
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1 10368 Games rolled with Variance Reduction. Dice Seed: 15098271 Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction. Dice Seed: 15098271 Moves: 3-ply, cube decisions: XG Roller
|
(m) Money 4-ply
| | White is Player 2
score: 0 pip: 119 | Unlimited Game Jacoby Beaver | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:0:3:0:10 |
Blue to play 11 |
1. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.156 |
| Player: Opponent: | 53.89% (G:14.52% B:0.90%) 46.11% (G:19.34% B:1.94%) | Conf.: ± 0.011 (+0.145...+0.166) - [100.0%] Duration: 9 hours 17 minutes |
|
2. | Rollout1 | 24/23 8/7 4/3*(2) | eq: +0.127 (-0.029) |
| Player: Opponent: | 53.29% (G:14.69% B:0.86%) 46.71% (G:16.67% B:1.14%) | Conf.: ± 0.006 (+0.122...+0.133) - [0.0%] Duration: 8 hours 58 minutes |
|
|
1 5184 Games rolled with Variance Reduction. Dice Seed: 31817346 Moves and cube decisions: 4-ply Search interval: Large
|
(d) DMP 3-ply
| | White is Player 2
score: 0 pip: 119 | 1 point match | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:0:0:1:10 |
Blue to play 11 |
1. | Rollout1 | 12/8 | eq: +0.102 |
| Player: Opponent: | 55.11% (G:11.30% B:1.07%) 44.89% (G:27.94% B:4.81%) | Conf.: ± 0.002 (+0.101...+0.104) - [100.0%] Duration: 4 hours 35 minutes |
|
2. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.092 (-0.011) |
| Player: Opponent: | 54.58% (G:13.34% B:1.64%) 45.42% (G:22.28% B:6.07%) | Conf.: ± 0.001 (+0.090...+0.093) - [0.0%] Duration: 4 hours 54 minutes |
|
3. | Rollout2 | 24/23 14/13 4/3*(2) | eq: +0.077 (-0.025) |
| Player: Opponent: | 53.84% (G:13.36% B:1.62%) 46.16% (G:20.79% B:4.15%) | Conf.: ± 0.003 (+0.074...+0.080) - [0.0%] Duration: 1 hour 20 minutes |
|
4. | Rollout2 | 24/23 8/7 4/3*(2) | eq: +0.076 (-0.026) |
| Player: Opponent: | 53.82% (G:14.70% B:1.70%) 46.18% (G:20.17% B:4.08%) | Conf.: ± 0.003 (+0.074...+0.079) - [0.0%] Duration: 1 hour 19 minutes |
|
5. | Rollout2 | 24/23 14/13 8/6 | eq: +0.070 (-0.032) |
| Player: Opponent: | 53.52% (G:11.35% B:1.05%) 46.48% (G:19.53% B:3.27%) | Conf.: ± 0.003 (+0.068...+0.073) - [0.0%] Duration: 1 hour 18 minutes |
|
6. | Rollout2 | 24/23 12/11(2) 8/7 | eq: +0.065 (-0.037) |
| Player: Opponent: | 53.27% (G:10.94% B:1.05%) 46.73% (G:23.49% B:5.06%) | Conf.: ± 0.003 (+0.063...+0.068) - [0.0%] Duration: 1 hour 22 minutes |
|
7. | Rollout2 | 24/23 8/5 | eq: +0.063 (-0.039) |
| Player: Opponent: | 53.14% (G:10.60% B:1.07%) 46.86% (G:23.13% B:4.78%) | Conf.: ± 0.003 (+0.060...+0.066) - [0.0%] Duration: 1 hour 12 minutes |
|
8. | Rollout2 | 24/23 13/12 4/3*(2) | eq: +0.054 (-0.049) |
| Player: Opponent: | 52.68% (G:12.92% B:1.52%) 47.32% (G:22.11% B:4.74%) | Conf.: ± 0.003 (+0.051...+0.056) - [0.0%] Duration: 1 hour 10 minutes |
|
9. | Rollout2 | 24/23 13/12 8/6 | eq: +0.045 (-0.058) |
| Player: Opponent: | 52.23% (G:11.03% B:1.08%) 47.77% (G:20.39% B:3.59%) | Conf.: ± 0.003 (+0.042...+0.047) - [0.0%] Duration: 1 hour 04 minutes |
|
10. | Rollout2 | 24/23 13/11 8/7 | eq: +0.027 (-0.075) |
| Player: Opponent: | 51.35% (G:10.20% B:0.94%) 48.65% (G:23.48% B:4.75%) | Conf.: ± 0.003 (+0.024...+0.030) - [0.0%] Duration: 1 hour 05 minutes |
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11. | Rollout2 | 4/3*(2) 3/2*(2) | eq: -0.014 (-0.116) |
| Player: Opponent: | 49.29% (G:21.06% B:3.36%) 50.71% (G:23.70% B:6.24%) | Conf.: ± 0.003 (-0.017...-0.011) - [0.0%] Duration: 1 hour 17 minutes |
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|
1 20736 Games rolled with Variance Reduction. Dice Seed: 81605744 Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction. Dice Seed: 81605744 Moves: 3-ply, cube decisions: XG Roller
|
(d) DMP 4-ply
| | White is Player 2
score: 0 pip: 119 | 1 point match | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:0:0:1:10 |
Blue to play 11 |
1. | Rollout1 | 12/8 | eq: +0.103 |
| Player: Opponent: | 55.17% (G:11.28% B:1.18%) 44.83% (G:27.87% B:4.41%) | Conf.: ± 0.003 (+0.101...+0.106) - [100.0%] Duration: 17 hours 05 minutes |
|
2. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.092 (-0.011) |
| Player: Opponent: | 54.62% (G:13.41% B:1.63%) 45.38% (G:21.99% B:6.35%) | Conf.: ± 0.002 (+0.090...+0.095) - [0.0%] Duration: 18 hours 58 minutes |
|
|
1 5184 Games rolled with Variance Reduction. Dice Seed: 31817346 Moves and cube decisions: 4-ply Search interval: Large
|
(s) Gammon Save 3-ply
| | White is Player 2
score: 0 pip: 119 | 2 point match Crawford | pip: 150 score: 1
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:1:0:1:2:10 |
Blue to play 11 |
1. | Rollout1 | 24/23 8/7 4/3*(2) | eq: -0.227 |
| Player: Opponent: | 51.49% (G:13.24% B:1.66%) 48.51% (G:12.85% B:2.24%) | Conf.: ± 0.001 (-0.228...-0.226) - [100.0%] Duration: 11 hours 59 minutes |
|
2. | Rollout1 | 24/23 14/13 8/6 | eq: -0.235 (-0.008) |
| Player: Opponent: | 51.17% (G:10.72% B:0.99%) 48.83% (G:12.93% B:2.66%) | Conf.: ± 0.001 (-0.236...-0.234) - [0.0%] Duration: 12 hours 02 minutes |
|
3. | Rollout2 | 24/23 14/13 4/3*(2) | eq: -0.250 (-0.023) |
| Player: Opponent: | 51.79% (G:12.33% B:1.52%) 48.21% (G:14.31% B:3.28%) | Conf.: ± 0.002 (-0.253...-0.248) - [0.0%] Duration: 3 hours 20 minutes |
|
4. | Rollout3 | 24/23 13/12 8/6 | eq: -0.275 (-0.048) |
| Player: Opponent: | 49.76% (G:10.17% B:0.97%) 50.24% (G:13.51% B:2.71%) | Conf.: ± 0.004 (-0.279...-0.271) - [0.0%] Duration: 56 minutes 47 seconds |
|
5. | Rollout3 | 24/23 12/11 4/3*(2) | eq: -0.275 (-0.048) |
| Player: Opponent: | 53.08% (G:12.34% B:1.42%) 46.92% (G:16.85% B:6.16%) | Conf.: ± 0.004 (-0.279...-0.271) - [0.0%] Duration: 56 minutes 21 seconds |
|
6. | Rollout3 | 24/23 8/5 | eq: -0.285 (-0.058) |
| Player: Opponent: | 50.86% (G:10.33% B:0.89%) 49.14% (G:15.12% B:4.12%) | Conf.: ± 0.004 (-0.289...-0.281) - [0.0%] Duration: 56 minutes 16 seconds |
|
7. | Rollout3 | 24/23 12/11(2) 8/7 | eq: -0.287 (-0.060) |
| Player: Opponent: | 50.39% (G:9.59% B:0.86%) 49.61% (G:14.75% B:3.98%) | Conf.: ± 0.004 (-0.291...-0.284) - [0.0%] Duration: 56 minutes 57 seconds |
|
8. | Rollout3 | 24/23 13/12 4/3*(2) | eq: -0.290 (-0.063) |
| Player: Opponent: | 50.59% (G:11.89% B:1.55%) 49.41% (G:15.07% B:3.82%) | Conf.: ± 0.004 (-0.293...-0.286) - [0.0%] Duration: 52 minutes 56 seconds |
|
9. | Rollout3 | 24/23 13/11 8/7 | eq: -0.335 (-0.108) |
| Player: Opponent: | 48.82% (G:9.22% B:0.85%) 51.18% (G:15.58% B:3.56%) | Conf.: ± 0.004 (-0.339...-0.331) - [0.0%] Duration: 47 minutes 27 seconds |
|
10. | Rollout3 | 24/23 14/12 8/7 | eq: -0.347 (-0.120) |
| Player: Opponent: | 46.67% (G:9.04% B:0.73%) 53.33% (G:14.03% B:2.64%) | Conf.: ± 0.004 (-0.351...-0.344) - [0.0%] Duration: 49 minutes 23 seconds |
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11. | Rollout3 | 24/23 14/13 12/11 8/7 | eq: -0.409 (-0.182) |
| Player: Opponent: | 45.68% (G:8.84% B:0.78%) 54.32% (G:16.13% B:3.65%) | Conf.: ± 0.004 (-0.412...-0.405) - [0.0%] Duration: 51 minutes 07 seconds |
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12. | Rollout3 | 12/8 | eq: -0.427 (-0.200) |
| Player: Opponent: | 54.09% (G:11.60% B:1.28%) 45.91% (G:25.45% B:4.09%) | Conf.: ± 0.006 (-0.433...-0.421) - [0.0%] Duration: 1 hour 03 minutes |
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13. | Rollout3 | 4/3*(2) 3/2*(2) | eq: -0.437 (-0.210) |
| Player: Opponent: | 48.45% (G:19.75% B:2.98%) 51.55% (G:20.30% B:4.00%) | Conf.: ± 0.004 (-0.442...-0.433) - [0.0%] Duration: 1 hour 02 minutes |
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1 62208 Games rolled with Variance Reduction. Dice Seed: 87348936 Moves: 3-ply, cube decisions: XG Roller
2 15552 Games rolled with Variance Reduction. Dice Seed: 87348936 Moves: 3-ply, cube decisions: XG Roller
3 5184 Games rolled with Variance Reduction. Dice Seed: 87348936 Moves: 3-ply, cube decisions: XG Roller
|
(s) Gammon Save 4-ply
| | White is Player 2
score: 0 pip: 119 | 2 point match Crawford | pip: 150 score: 1
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:1:0:1:2:10 |
Blue to play 11 |
1. | Rollout1 | 24/23 8/7 4/3*(2) | eq: -0.223 |
| Player: Opponent: | 51.38% (G:12.70% B:1.60%) 48.62% (G:12.54% B:2.14%) | Conf.: ± 0.002 (-0.225...-0.222) - [100.0%] Duration: 1 day 16 hours 44 minutes |
|
2. | Rollout1 | 24/23 14/13 8/6 | eq: -0.232 (-0.009) |
| Player: Opponent: | 51.21% (G:10.68% B:0.88%) 48.79% (G:12.81% B:2.74%) | Conf.: ± 0.002 (-0.234...-0.230) - [0.0%] Duration: 1 day 14 hours 35 minutes |
|
|
1 12960 Games rolled with Variance Reduction. Dice Seed: 31817346 Moves and cube decisions: 4-ply Search interval: Large
|
(g) Gammon Go 3-ply
| | White is Player 2
score: 1 pip: 119 | 2 point match Crawford | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:1:1:2:10 |
Blue to play 11 |
1. | Rollout1 | 4/3*(2) 3/2*(2) | eq: +0.411 |
| Player: Opponent: | 48.46% (G:22.07% B:3.87%) 51.54% (G:25.45% B:7.48%) | Conf.: ± 0.003 (+0.408...+0.413) - [100.0%] Duration: 3 hours 14 minutes |
|
2. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.397 (-0.013) |
| Player: Opponent: | 53.19% (G:16.68% B:2.24%) 46.81% (G:23.63% B:6.90%) | Conf.: ± 0.002 (+0.395...+0.400) - [0.0%] Duration: 3 hours 24 minutes |
|
3. | Rollout1 | 24/23 8/7 4/3*(2) | eq: +0.396 (-0.015) |
| Player: Opponent: | 52.78% (G:17.03% B:2.33%) 47.22% (G:21.30% B:4.51%) | Conf.: ± 0.002 (+0.394...+0.398) - [0.0%] Duration: 3 hours 09 minutes |
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4. | Rollout2 | 24/23 14/13 4/3*(2) | eq: +0.377 (-0.033) |
| Player: Opponent: | 53.01% (G:15.86% B:2.14%) 46.99% (G:21.48% B:4.33%) | Conf.: ± 0.004 (+0.373...+0.381) - [0.0%] Duration: 54 minutes 36 seconds |
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5. | Rollout2 | 12/8 | eq: +0.373 (-0.037) |
| Player: Opponent: | 54.03% (G:14.64% B:1.57%) 45.97% (G:28.15% B:4.83%) | Conf.: ± 0.005 (+0.369...+0.378) - [0.0%] Duration: 59 minutes 03 seconds |
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6. | Rollout2 | 24/23 13/12 4/3*(2) | eq: +0.347 (-0.064) |
| Player: Opponent: | 51.58% (G:15.76% B:2.04%) 48.42% (G:23.09% B:5.18%) | Conf.: ± 0.004 (+0.343...+0.351) - [0.0%] Duration: 50 minutes 24 seconds |
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|
1 15552 Games rolled with Variance Reduction. Dice Seed: 15098271 Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction. Dice Seed: 15098271 Moves: 3-ply, cube decisions: XG Roller
|
(g) Gammon Go 4-ply
| | White is Player 2
score: 1 pip: 119 | 2 point match Crawford | pip: 150 score: 0
Blue is Player 1 | |
XGID=--aaBBBBA---BAA-aacbbbbAA-:0:0:1:11:0:1:1:2:10 |
Blue to play 11 |
1. | Rollout1 | 4/3*(2) 3/2*(2) | eq: +0.413 |
| Player: Opponent: | 48.66% (G:21.97% B:3.70%) 51.34% (G:24.48% B:6.91%) | Conf.: ± 0.004 (+0.409...+0.416) - [100.0%] Duration: 17 hours 28 minutes |
|
2. | Rollout1 | 24/23 12/11 4/3*(2) | eq: +0.400 (-0.013) |
| Player: Opponent: | 53.32% (G:16.67% B:2.20%) 46.68% (G:23.00% B:7.15%) | Conf.: ± 0.003 (+0.397...+0.403) - [0.0%] Duration: 17 hours 55 minutes |
|
3. | Rollout1 | 24/23 8/7 4/3*(2) | eq: +0.398 (-0.014) |
| Player: Opponent: | 53.02% (G:16.90% B:2.20%) 46.98% (G:21.05% B:4.37%) | Conf.: ± 0.003 (+0.395...+0.401) - [0.0%] Duration: 18 hours 14 minutes |
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1 5184 Games rolled with Variance Reduction. Dice Seed: 31817346 Moves and cube decisions: 4-ply Search interval: Large
|