I had this position recently on Galaxy. Trailer's tp will be their MWC if they pass due to the auto recube to 8. Their MWC at 7a-Crawford is ~9%, so that's White's tp. Does White have a take?
Most racing formulas are designed for unlimited games so they will all tell you that 38-51 is a clear R/P. Here we need to know whether or not White will win at least 9%. The formula that I use for estimating winning chances at lopsided scores like this is the Kleinman formula. It is based on D (the difference in the two pip counts) and S (the sum of the two). The formula is D squared/S. You first subtract 4 pips from the side on roll before figuring what D and S are. So 38-51 becomes 34-51. D is then 17 and S is 85. D squared/S will be 289/85 which is 3.40.
A ratio of 3.0 gives the side on roll about 89% while 4.0 raises that to 92%. 3.4 should then be ~90.2%. The formula therefore says that White has a close take. Should Blue recube?
When you're this close to the opponent's tp, it's almost always a good cube. ATS though the leader's doubling window is real small. You just use risk/risk+gain to figure the minimum doubling point. If you lose 2/8 points in this game, your MWC will be 65%/0%, so the risk is 65. On the gain side, winning 2/8 points gives you 91%/100% MWC, so the gain is 9.
The minimum redoubling point is then 65/74 which is close to 88%. That's the low end of the doubling window while the high end is when the trailer has a marginal t/p which will be 91%. When the leader's winning chances are between 88% and 91%, he can consider redoubling. The closer these are to the top end, the more likely a recube is correct.
Anyway it went R/P over the board. I didn't estimate the EPC's over the board due to time constraints but I did afterwards and estimated that Blue would waste about .5 pips more than White. This might be enough to make it a no redouble but there's another detail to think about. That's the type of bearoff each side has.
Art Benjamin has written a lot about cubes in different types of bearoffs in the USBGF Primetime magazine. He would say that White has a high variance position while Blue has a medium. A medium on roll vs. a high has slightly better winning chances than in a high vs. high, given the same EPC's in both. This vig probably cancels out some or all of the .5 extra wastage that Blue has in the EPC, so I would stick with using the Kleinman winning chance estimate of 90.2%.
It's pretty accurate in this position:
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| XGID=-AA-BCB------------ebba---:1:1:1:00:4:0:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 90.54% (G:0.00% B:0.00%) | 90.48% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 9.46% (G:0.00% B:0.00%) | 9.52% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.811 | +1.349 |
| Cubeful Equities | ||
| No redouble: | +0.915 (-0.066) | ±0.001 (+0.914..+0.917) |
| Redouble/Take: | +0.982 | ±0.000 (+0.981..+0.982) |
| Redouble/Pass: | +1.000 (+0.018) | |
| 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: 5.8 seconds | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2