"Not quite right Phil. Let's say you have a 5 roll position with an EPC of 36. Oppt's point of last take is with an EPC of 38."
Should specify 38 if it is for a low wastage postion.
" his winning chances go from 50% to roughly 22%. "
Does the 22% work for a short race? Also the point of last take is a rounded value and might not be right on the edge of take/pass. Consider the following position which is a very easy take and has EPC of 36.0 to 37.95
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| XGID=-J-----------------babb---:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 75.504% (G:0.000% B:0.000%) | 75.495% (G:0.000% B:0.000%) |
| Opponent Winning Chances: | 24.496% (G:0.000% B:0.000%) | 24.505% (G:0.000% B:0.000%) |
| Cubeless Equities | +0.5101 | +1.0198 |
| Cubeful Equities | ||
| No double: | +0.7458 (-0.1741) | ±0.0023 (+0.7434..+0.7481) |
| Double/Take: | +0.9199 | ±0.0031 (+0.9167..+0.9230) |
| Double/Pass: | +1.0000 (+0.0801) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.9 second | ||
eXtreme Gammon Version: 2.03
Adding a real pip makes the EPC 38.81 and now a solid pass.
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| XGID=-J-----------------bbab---:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 78.235% (G:0.000% B:0.000%) | 78.233% (G:0.000% B:0.000%) |
| Opponent Winning Chances: | 21.765% (G:0.000% B:0.000%) | 21.767% (G:0.000% B:0.000%) |
| Cubeless Equities | +0.5647 | +1.1293 |
| Cubeful Equities | ||
| No double: | +0.8042 (-0.1958) | ±0.0024 (+0.8018..+0.8066) |
| Double/Take: | +1.0470 (+0.0470) | ±0.0031 (+1.0439..+1.0501) |
| Double/Pass: | +1.0000 | |
| Best Cube action: Double / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.6 second | ||
eXtreme Gammon Version: 2.03
Interpolating gives a good estimate of what the last take EPC is and also what win% matches that last take. The equity of 1 is 63.02% of the way from take equities of .9199 to 1.047. Going 63.02% of the way from win % of 75.495 to 78.235% gives only 76.51 (significantly lower than 78) and going 62.02% of the way from EPC of 37.95 to 38.81 gives EPC of 38.27 (a bit higher than 38 as expected).