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| XGID=-a-aB-DaC-B-bBbc--Ab-c--A-:0:0:1:51:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
The original problem (with cube centered) is shown above. Blue on roll, has a 51 to play. (Rollout summaries and details can be seen here.). The rest of this post responds to Tim's inquiry:
........After K, what does the cube action look like after a weak response?
Below are (nacubracs) for cube decisions that arise after Blue plays K (Kill, 8/7* 8/3*), and White rolls/plays F (Fans), 5 (enters on the 5pt), 3 (enters on the 3pt), or 1 (enters on the 1pt). These positions are in ascending order of strength from White's perspective, and descending order from Blue's perspective.
There are two relevant cube placements. Either the cube is still centered (see the first set of brackets in each row) or Blue owns the cube (the second brackets). The first group has evaluations; the second group has rollout results.
Evaluations (XGR++)
........If White F ...[D 1495–553] ....[X 1058+437]
........If White 5.....[D 1103–351] ....[R 1104–227]
........If White 2.....[D 1003–228] ....[R 1005–145]
........If White 1.......[D 770–37] ........[X 779–13]
ROLLOUTS (moves 3-ply, cube decisions XGR)
........If White F ................................[X 1032+400] 5
........If White 5 .................................[R 1055–140] 5
........If White 2 ...................................[R 953–119] 5
........If White 1 ......[N 705–5] 25 .......[X 754–43] 5
Cube action letter: D = Double, N = No double, R = Redouble, X = no redouble.
Equities are in thousandths of a point and if the cube is given (D or R) then a take is assumed (pass = 1000 always, too obvious to list).
After the minus sign is the size of the error if Blue chooses the opposite/wrong action (e.g., N or R in the fourth row). [Exception: If too good to double, the error for doubling is already implied by the difference from 1000; instead add the + number to get the additional information of the terrible-take equity.]
Explanation of nacubracs
If the number to the left of the minus sign is close to 1000, or if the number on the right of the minus sign is small, a close cube decision is involved.
As you can see in the chart above, XG's evaluation is optimistic for Blue (1.058 vs 1.032, 1.104 vs 1.055, 1.005 vs .953, .770 vs .705, and .779 vs .754) for all five of the cube decisions I rolled out. [For the fourth position, this optimism causes XG to double early.]
For further clarification, row by row: (1) The X being over 1000 tells you Blue is too good to redouble. (2) The D or R over 1000 tells you it's double/pass or redouble/pass. (3) The D or R under 1000 tells you it's double/take or redouble/take. (4) The N and X tells you the position is not good enough for Blue to double or redouble (as the number is under 1000).
Detailed rollout results are shown below.
Nack
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| XGID=ba-AB-DAA-B-bBbc--Ab-c--A-:1:1:1:00:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 71.71% (G:43.37% B:2.86%) | 71.48% (G:43.78% B:3.05%) |
| Opponent Winning Chances: | 28.29% (G:5.79% B:0.33%) | 28.52% (G:5.93% B:0.38%) |
| Cubeless Equities | +0.835 | +1.669 |
| Cubeful Equities | ||
| No redouble: | +1.032 | ±0.006 (+1.025..+1.038) |
| Redouble/Take: | +1.431 (+0.400) | ±0.011 (+1.420..+1.443) |
| Redouble/Pass: | +1.000 (-0.032) | |
| Best Cube action: Too good to redouble / Pass | ||
| Percentage of wrong take needed to make the double decision right: 7.3% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 hour 56 minutes | ||
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| XGID=aa-ABaDAA-B-bBbc--Ab-c--A-:1:1:1:00:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 67.46% (G:36.44% B:2.39%) | 67.28% (G:36.75% B:2.64%) |
| Opponent Winning Chances: | 32.54% (G:7.63% B:0.49%) | 32.72% (G:7.72% B:0.49%) |
| Cubeless Equities | +0.656 | +1.315 |
| Cubeful Equities | ||
| No redouble: | +0.860 (-0.140) | ±0.006 (+0.854..+0.866) |
| Redouble/Take: | +1.055 (+0.055) | ±0.012 (+1.043..+1.067) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 3 hours 55 minutes | ||
 |
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| XGID=aaaAB-DAA-B-bBbc--Ab-c--A-:1:1:1:00:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 65.85% (G:35.55% B:2.54%) | 65.68% (G:36.16% B:2.79%) |
| Opponent Winning Chances: | 34.15% (G:8.20% B:0.50%) | 34.32% (G:8.39% B:0.51%) |
| Cubeless Equities | +0.611 | +1.228 |
| Cubeful Equities | ||
| No redouble: | +0.833 (-0.119) | ±0.007 (+0.827..+0.840) |
| Redouble/Take: | +0.953 | ±0.012 (+0.941..+0.965) |
| Redouble/Pass: | +1.000 (+0.047) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 hour 53 minutes | ||
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| XGID=ab-AB-DAA-B-bBbc--Ab-c--A-:0:0:1:00:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 64.05% (G:27.62% B:2.99%) | 63.88% (G:27.68% B:3.22%) |
| Opponent Winning Chances: | 35.95% (G:8.31% B:0.44%) | 36.12% (G:8.54% B:0.46%) |
| Cubeless Equities | +0.500 | +0.993 |
| Cubeful Equities | ||
| No double: | +0.705 | ±0.004 (+0.702..+0.709) |
| Double/Take: | +0.701 (-0.005) | ±0.005 (+0.695..+0.706) |
| Double/Pass: | +1.000 (+0.295) | |
| Best Cube action: No double / Take | ||
| Percentage of wrong pass needed to make the double decision right: 1.5% | ||
| Rollout details | ||
| 25920 Games rolled with Variance Reduction. Dice Seed: 90634172 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 91.5% | |
| Take Decision confidence: | 100.0% | |
| Duration: 13 hours 25 minutes | ||
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| XGID=ab-AB-DAA-B-bBbc--Ab-c--A-:1:1:1:00:0:0:3:0:10 | |||||
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 64.02% (G:27.70% B:3.04%) | 63.88% (G:27.81% B:3.28%) |
| Opponent Winning Chances: | 35.98% (G:8.43% B:0.48%) | 36.12% (G:8.51% B:0.47%) |
| Cubeless Equities | +0.499 | +0.997 |
| Cubeful Equities | ||
| No redouble: | +0.754 | ±0.007 (+0.747..+0.761) |
| Redouble/Take: | +0.711 (-0.043) | ±0.012 (+0.699..+0.722) |
| Redouble/Pass: | +1.000 (+0.246) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 12.9% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 2 hours 46 minutes | ||
The last two diagrams can be viewed side-by-side, if you widen your window.