This is a pips vs rolls position. Need to estimate the EPC's to determine the correct cube action. First the pips position: If all of that side's checkers were on the 4-5-6 points, the EPC would be the raw pip count plus 5.5 to 7 pips. 5.5 with only a few checkers remaining, 7 with all 15.
Here we don't have any checkers on the 5 and we do have two on the 3 so the above formula might be off a bit. Art Benjamin has created an EPC formula that's extremely accurate for positions with 5-8 checkers. He calls it "Modified Matussek." The formula is pip count + 2 + .2(# of checkers on 5) + .4(# on 4) + .8(# on 3) + 1.3 (# on 2) + 2 (# on 1) + .7(# of empty points) + .3(# of checkers on the most stacked point). Here that totals 35.0.
This formula is very accurate with an average error rating of .22 pips. It doesn't apply to scrunched positions where there are no checkers on the 5 or 6 points.
Now for the rolls side. If all 9 checkers were on the ace point, then the EPC would be 36. The EPC must be marginally higher here since double 1s followed by a single ace will be a miss. The rolls side will also miss if they roll 5 consecutive single aces. The rolls side has an odd number of checkers so they can afford one miss. The EPC is a shade over 36.
So the EPC's are 35 to 36. 35 is almost a 5-roll position. Trice's rule for this type of position is that the underdog's point of last take is when trailing by leader's rolls -3 pips. So the POLT is when trailing by a little less than 2 pips. Here's he's trailing by a little over 1. The leader can redouble if his lead is within 1 pip of the POLT.
The side on roll's lead is less than 1 pip away from the POLT, so the answer for money is R/T.
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| XGID=---BA-C---------------beb-:1:1:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 74.41% (G:0.00% B:0.00%) | 74.40% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 25.59% (G:0.00% B:0.00%) | 25.60% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.488 | +0.976 |
| Cubeful Equities | ||
| No redouble: | +0.750 (-0.116) | ±0.003 (+0.747..+0.753) |
| Redouble/Take: | +0.866 | ±0.003 (+0.863..+0.870) |
| Redouble/Pass: | +1.000 (+0.134) | |
| Best Cube action: Redouble / Take | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. First 12 moves: 3-ply, cube decisions: XG Roller Remaining moves: 3-ply Red, cube decisions: 4-ply Search interval: Large | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.8 second | ||
eXtreme Gammon Version: 2.10
Now for this 4a-5a match score. 5a's tp ats is 25.64%. The rollout shows this to be a small pass with 25.59% winning chances.
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| XGID=---BA-C---------------beb-:1:1:1:00:3:2:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 74.41% (G:0.00% B:0.00%) | 74.41% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 25.59% (G:0.00% B:0.00%) | 25.59% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.488 | +1.305 |
| Cubeful Equities | ||
| No redouble: | +0.763 (-0.237) | ±0.002 (+0.761..+0.765) |
| Redouble/Take: | +1.003 (+0.003) | ±0.000 (+1.003..+1.003) |
| Redouble/Pass: | +1.000 | |
| Best Cube action: Redouble / Pass | ||
| Rollout details | ||
| 1296 Games rolled with Variance Reduction. First 12 moves: 3-ply, cube decisions: XG Roller Remaining moves: 3-ply Red, cube decisions: 4-ply Search interval: Large | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 0.9 second | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2