The original thread for this position was initiated ten days ago. Please forgive the delay in posting rollouts.
My construction of this position was loosely inspired by Ian Terry's post (just after Christmas). The position there, by the way, appears to have been reached by 41S-21S-66P-64R-43 (though if so, 66P is a whopper). For Blue, I moved one 1pt checker to the midpoint and the other to the 21pt, and a 6pt spare to the 8pt. For White, I used a midpoint spare and all three 6pt spares to add her 10pt and 3pt.
Seven bgonliners weighed in on this "interesting and instructive position" (PW's kind description): Igor, Casper, Ah Clem, Paul Weaver, Chuck, Neil Kaz and Keene (in order of response).
With so many plausible ways to play 43, five (of the seven) repondents chose different plays at all four scores, though three of them admitted (or implied) that my tendency to post four-score positions affected at least one of the moves they would likely have otherwise played OTB.
Money (i.e., Unlimited or "normal" scores) attracted the greatest diversity. A minority of three respondents chose P (Point, 9/5 8/5), which tops the rollout. Two (though three OTB) chose second-best H (Hit, 21/14*), and one chose K (Kill, 13/10* 6/2*). Finally, one respondent chose the interesting Z (reverse split, 24/21 13/9), which was selected by a total of four respondents (and almost a fifth) at some score.
At DMP, six of the seven respondents chose the logical H (Hit, 21/14*). One respondent found the creative C (Cross, 24/21 9/5), though possibly it was a typo and he meant Z. I will add C to the DMP rollout on request, although XGR++ evaluates it as ninth best and –.054.
At Gammon Save, it was pretty much a split decision between the rollout winner @ (anchor, 24/20 23/20) and Z (24/21 13/9, an anchoring alternative). @ took four votes, and Z took three, but it could have easily gone the other way as Casper seemed close to picking Z, a move Chuck supported with cogent analysis. [Note: If we move one of Blue's 8pt spares back to the midpoint, then Z edges out @ at gammon save, but a new play D (Down, 13/10* 13/9) becomes best at all scores! (XGR++ evaluation.)]
At Gammon Go, K (Kill, 13/10* 6/2*) was chosen by six respondents (the seventh went with P). Keene did choose K but seemed tentative, perhaps because the second hit is so low and leaves only one spare on the 6pt. That said, K has enough going for it that it also rolled out at second best at DMP.
Below are the seven sets of answers (m = money, d = DMP, s = gammon save, g = gammon go), by respondent (names omitted). The sets that most closely match the rollout results are listed first.
.....m..d..s..g
.....P..H..@..K
.....P..H..@..K
.....K..H..@..K
.....P..H..Z..K
.....H..H..Z..K
.....Z..H..@..P
.....H..C..Z..K
The candidates for playing 43 in this position have many competing strengths. Seven different plays (@, D, H, K, P, X, Z) roll out in the top three at some score. On the whole, I think the respondents did well sorting it out.
Here is a nacbrac summary of the rollouts (one line for each score):
.........m[P H17 X36 K38 D40 @49 Z59 T68] "<=31*5
..........d[H K10 D14 X15 P20 T45 @45 Z49] "<=12*7*5
..........s[@ Z29 P61 H98 T128 C132 X136 D138 K145] "<=5
..........g[K P16 H18 D23 X34 T57 o81 O84 Z85 @98] "<=10***5
Nactation key -- alphabetical:..@ (anchor) = 24/20 23/20, C (Cross) = 24/21 9/5, D (Down) = 13/10* 13/9, H (Hit) = 21/14*, K (Kill) = 13/10* 6/2*, o (outer) = 13/10* 9/5, O = 13/10* 8/4, P = Point (9/5 8/5), T (sTack/Tower) = 13/10*/6, X (hit and split) = 24/20 13/10*, Z (reverse split) = 24/21 13/9.....Nactation tutorial ....nacbracs explanation
Yes, as some correctly guessed, each of the four main scores has a different best play. In fact, this is not only a T4 (technical four-score position). It is also an "R4" (real four-score position), meaning that for each of money, DMP, gammon save and gammon go, the best play clears its respective .010, .0045, .007 and .007 "tied" margin (compared to any play that is best at some other score).
The power rating for this R4 is [sqrt 17 + sqrt 20*10/9 + sqrt 10*61/7 + sqrt 10*16/7] = 22.95. To compare to the power ratings of other R4's, click here and scroll to the bottom. Not included in that consolidation is an R4 with a roll of 41.
For the 43 position, detailed rollout results follow.
Nack
Money
          
 
        
 | | White is Player 2
score: 0
pip: 150 | Unlimited Game
Jacoby Beaver | pip: 172
score: 0
Blue is Player 1 |
|
| XGID=--a---D-DAa-cCab-c-b-AbAA-:0:0:1:43:0:0:3:0:10 |
| Blue to play 43 |
| 1. | Rollout1 | 9/5 8/5 | eq: -0.324 |
| Player:
Opponent: | 41.69% (G:11.65% B:0.45%)
58.31% (G:15.75% B:0.97%) | Conf.: ± 0.003 (-0.328...-0.321) - [100.0%]
Duration: 17 hours 09 minutes |
|
| 2. | Rollout1 | 21/14* | eq: -0.342 (-0.017) |
| Player:
Opponent: | 42.74% (G:10.99% B:0.52%)
57.26% (G:18.74% B:1.34%) | Conf.: ± 0.004 (-0.345...-0.338) - [0.0%]
Duration: 21 hours 53 minutes |
|
| 3. | Rollout2 | 24/20 13/10* | eq: -0.361 (-0.036) |
| Player:
Opponent: | 41.92% (G:11.02% B:0.56%)
58.08% (G:19.47% B:1.55%) | Conf.: ± 0.008 (-0.369...-0.352) - [0.0%]
Duration: 2 hours 53 minutes |
|
| 4. | Rollout3 | 13/10* 6/2* | eq: -0.363 (-0.038) |
| Player:
Opponent: | 42.07% (G:12.41% B:0.58%)
57.93% (G:20.63% B:1.81%) | Conf.: ± 0.009 (-0.372...-0.353) - [0.0%]
Duration: 2 hours 22 minutes |
|
| 5. | Rollout2 | 13/9 13/10* | eq: -0.364 (-0.040) |
| Player:
Opponent: | 41.95% (G:11.68% B:0.68%)
58.05% (G:19.86% B:1.79%) | Conf.: ± 0.010 (-0.374...-0.354) - [0.0%]
Duration: 2 hours 54 minutes |
|
| 6. | Rollout3 | 24/20 23/20 | eq: -0.373 (-0.048) |
| Player:
Opponent: | 40.19% (G:8.95% B:0.30%)
59.81% (G:12.48% B:0.47%) | Conf.: ± 0.007 (-0.380...-0.366) - [0.0%]
Duration: 2 hours 23 minutes |
|
| 7. | Rollout3 | 24/21 13/9 | eq: -0.384 (-0.059) |
| Player:
Opponent: | 39.94% (G:9.57% B:0.38%)
60.06% (G:13.03% B:0.58%) | Conf.: ± 0.008 (-0.392...-0.376) - [0.0%]
Duration: 2 hours 21 minutes |
|
| 8. | Rollout2 | 13/10* 10/6 | eq: -0.392 (-0.068) |
| Player:
Opponent: | 40.65% (G:11.19% B:0.53%)
59.35% (G:17.86% B:1.21%) | Conf.: ± 0.008 (-0.401...-0.384) - [0.0%]
Duration: 2 hours 48 minutes |
|
| |
1 31104 Games rolled with Variance Reduction.
Dice Seed: 81984670
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
3 5184 Games rolled with Variance Reduction.
Dice Seed: 81984670
Moves: 3-ply, cube decisions: XG Roller
|
DMP
| | White is Player 2
score: 0
pip: 150 | | 1 point match | pip: 172
score: 0
Blue is Player 1 |
|
| XGID=--a---D-DAa-cCab-c-b-AbAA-:0:0:1:43:0:0:0:1:10 |
| Blue to play 43 |
| 1. | Rollout1 | 21/14* | eq: -0.134 |
| Player:
Opponent: | 43.30% (G:11.91% B:1.52%)
56.70% (G:23.03% B:4.82%) | Conf.: ± 0.002 (-0.136...-0.132) - [100.0%]
Duration: 3 hours 50 minutes |
|
| 2. | Rollout1 | 13/10* 6/2* | eq: -0.144 (-0.010) |
| Player:
Opponent: | 42.81% (G:13.05% B:1.75%)
57.19% (G:25.36% B:5.86%) | Conf.: ± 0.002 (-0.146...-0.141) - [0.0%]
Duration: 4 hours 01 minute |
|
| 3. | Rollout2 | 13/9 13/10* | eq: -0.148 (-0.014) |
| Player:
Opponent: | 42.58% (G:12.91% B:1.93%)
57.42% (G:24.45% B:5.64%) | Conf.: ± 0.003 (-0.151...-0.145) - [0.0%]
Duration: 3 hours 00 minute |
|
| 4. | Rollout2 | 24/20 13/10* | eq: -0.149 (-0.015) |
| Player:
Opponent: | 42.57% (G:12.19% B:1.81%)
57.43% (G:24.40% B:4.40%) | Conf.: ± 0.003 (-0.151...-0.146) - [0.0%]
Duration: 3 hours 03 minutes |
|
| 5. | Rollout3 | 9/5 8/5 | eq: -0.154 (-0.020) |
| Player:
Opponent: | 42.30% (G:12.00% B:1.25%)
57.70% (G:20.23% B:3.53%) | Conf.: ± 0.003 (-0.157...-0.151) - [0.0%]
Duration: 2 hours 06 minutes |
|
| 6. | Rollout4 | 13/10* 10/6 | eq: -0.179 (-0.045) |
| Player:
Opponent: | 41.06% (G:11.96% B:1.38%)
58.94% (G:22.23% B:4.56%) | Conf.: ± 0.003 (-0.182...-0.176) - [0.0%]
Duration: 3 hours 34 minutes |
|
| 7. | Rollout3 | 24/20 23/20 | eq: -0.179 (-0.045) |
| Player:
Opponent: | 41.03% (G:8.91% B:0.87%)
58.97% (G:19.04% B:1.85%) | Conf.: ± 0.003 (-0.182...-0.176) - [0.0%]
Duration: 2 hours 25 minutes |
|
| 8. | Rollout3 | 24/21 13/9 | eq: -0.183 (-0.049) |
| Player:
Opponent: | 40.86% (G:10.05% B:1.12%)
59.14% (G:19.04% B:1.85%) | Conf.: ± 0.003 (-0.186...-0.180) - [0.0%]
Duration: 2 hours 18 minutes |
|
| |
1 12960 Games rolled with Variance Reduction.
Dice Seed: 87955419
Moves: 3-ply, cube decisions: XG Roller
2 7776 Games rolled with Variance Reduction.
Dice Seed: 87955419
Moves: 3-ply, cube decisions: XG Roller
3 5184 Games rolled with Variance Reduction.
Dice Seed: 87955419
Moves: 3-ply, cube decisions: XG Roller
4 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
Gammon Save
| | White is Player 2
score: 0
pip: 150 | 2 point match
Crawford | pip: 172
score: 1
Blue is Player 1 |
|
| XGID=--a---D-DAa-cCab-c-b-AbAA-:0:0:1:43:1:0:1:2:10 |
| Blue to play 43 |
| 1. | Rollout1 | 24/20 23/20 | eq: -0.411 |
| Player:
Opponent: | 37.82% (G:7.46% B:0.86%)
62.18% (G:8.39% B:0.76%) | Conf.: ± 0.003 (-0.415...-0.408) - [100.0%]
Duration: 5 hours 34 minutes |
|
| 2. | Rollout1 | 24/21 13/9 | eq: -0.440 (-0.029) |
| Player:
Opponent: | 38.32% (G:9.10% B:0.85%)
61.68% (G:10.35% B:1.05%) | Conf.: ± 0.004 (-0.444...-0.437) - [0.0%]
Duration: 5 hours 03 minutes |
|
| 3. | Rollout1 | 9/5 8/5 | eq: -0.473 (-0.061) |
| Player:
Opponent: | 41.18% (G:12.26% B:1.49%)
58.82% (G:14.83% B:2.25%) | Conf.: ± 0.004 (-0.477...-0.469) - [0.0%]
Duration: 2 hours 19 minutes |
|
| 4. | Rollout1 | 21/14* | eq: -0.509 (-0.098) |
| Player:
Opponent: | 41.57% (G:11.78% B:1.63%)
58.43% (G:17.03% B:3.15%) | Conf.: ± 0.004 (-0.513...-0.505) - [0.0%]
Duration: 2 hours 51 minutes |
|
| 5. | Rollout1 | 13/10* 10/6 | eq: -0.540 (-0.128) |
| Player:
Opponent: | 40.24% (G:13.27% B:1.74%)
59.76% (G:17.23% B:3.22%) | Conf.: ± 0.004 (-0.544...-0.536) - [0.0%]
Duration: 2 hours 43 minutes |
|
| 6. | Rollout1 | 24/21 9/5 | eq: -0.543 (-0.132) |
| Player:
Opponent: | 35.31% (G:7.42% B:0.71%)
64.69% (G:12.46% B:1.47%) | Conf.: ± 0.004 (-0.547...-0.539) - [0.0%]
Duration: 2 hours 36 minutes |
|
| 7. | Rollout1 | 24/20 13/10* | eq: -0.547 (-0.136) |
| Player:
Opponent: | 40.82% (G:11.95% B:1.73%)
59.18% (G:18.19% B:3.97%) | Conf.: ± 0.005 (-0.552...-0.543) - [0.0%]
Duration: 2 hours 55 minutes |
|
| 8. | Rollout1 | 13/9 13/10* | eq: -0.549 (-0.138) |
| Player:
Opponent: | 41.00% (G:12.81% B:1.80%)
59.00% (G:18.47% B:4.30%) | Conf.: ± 0.005 (-0.554...-0.545) - [0.0%]
Duration: 2 hours 50 minutes |
|
| 9. | Rollout1 | 13/10* 6/2* | eq: -0.557 (-0.145) |
| Player:
Opponent: | 41.09% (G:13.08% B:1.77%)
58.91% (G:18.93% B:4.51%) | Conf.: ± 0.005 (-0.562...-0.552) - [0.0%]
Duration: 2 hours 56 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
Gammon Go
| | White is Player 2
score: 1
pip: 150 | 2 point match
Crawford | pip: 172
score: 0
Blue is Player 1 |
|
| XGID=--a---D-DAa-cCab-c-b-AbAA-:0:0:1:43:0:1:1:2:10 |
| Blue to play 43 |
| 1. | Rollout1 | 13/10* 6/2* | eq: +0.108 |
| Player:
Opponent: | 42.97% (G:12.44% B:1.38%)
57.03% (G:25.40% B:5.77%) | Conf.: ± 0.003 (+0.105...+0.112) - [100.0%]
Duration: 11 hours 30 minutes |
|
| 2. | Rollout1 | 9/5 8/5 | eq: +0.092 (-0.016) |
| Player:
Opponent: | 42.16% (G:12.44% B:0.98%)
57.84% (G:20.84% B:3.54%) | Conf.: ± 0.003 (+0.089...+0.095) - [0.0%]
Duration: 8 hours 21 minutes |
|
| 3. | Rollout1 | 21/14* | eq: +0.090 (-0.018) |
| Player:
Opponent: | 43.34% (G:11.17% B:1.20%)
56.66% (G:23.35% B:4.59%) | Conf.: ± 0.004 (+0.087...+0.094) - [0.0%]
Duration: 11 hours 06 minutes |
|
| 4. | Rollout1 | 13/9 13/10* | eq: +0.086 (-0.023) |
| Player:
Opponent: | 42.86% (G:11.42% B:1.59%)
57.14% (G:24.40% B:5.39%) | Conf.: ± 0.003 (+0.082...+0.089) - [0.0%]
Duration: 10 hours 46 minutes |
|
| 5. | Rollout2 | 24/20 13/10* | eq: +0.074 (-0.034) |
| Player:
Opponent: | 42.78% (G:10.91% B:1.41%)
57.22% (G:24.90% B:4.80%) | Conf.: ± 0.005 (+0.069...+0.079) - [0.0%]
Duration: 4 hours 08 minutes |
|
| 6. | Rollout2 | 13/10* 10/6 | eq: +0.051 (-0.057) |
| Player:
Opponent: | 41.32% (G:11.22% B:1.29%)
58.68% (G:22.28% B:4.57%) | Conf.: ± 0.004 (+0.047...+0.055) - [0.0%]
Duration: 3 hours 47 minutes |
|
| 7. | Rollout2 | 13/10* 9/5 | eq: +0.027 (-0.081) |
| Player:
Opponent: | 40.98% (G:10.39% B:1.28%)
59.02% (G:28.85% B:7.84%) | Conf.: ± 0.005 (+0.022...+0.032) - [0.0%]
Duration: 4 hours 24 minutes |
|
| 8. | Rollout2 | 13/10* 8/4 | eq: +0.024 (-0.084) |
| Player:
Opponent: | 40.85% (G:10.33% B:1.37%)
59.15% (G:30.55% B:8.20%) | Conf.: ± 0.005 (+0.019...+0.029) - [0.0%]
Duration: 4 hours 35 minutes |
|
| 9. | Rollout2 | 24/21 13/9 | eq: +0.023 (-0.085) |
| Player:
Opponent: | 40.75% (G:10.42% B:0.74%)
59.25% (G:20.09% B:1.94%) | Conf.: ± 0.004 (+0.019...+0.027) - [0.0%]
Duration: 3 hours 31 minutes |
|
| 10. | Rollout2 | 24/20 23/20 | eq: +0.011 (-0.098) |
| Player:
Opponent: | 40.66% (G:9.86% B:0.67%)
59.34% (G:19.63% B:1.96%) | Conf.: ± 0.004 (+0.006...+0.015) - [0.0%]
Duration: 3 hours 46 minutes |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|