Chuck,
Sorry for not responding promptly, I was shattered last night!
"I don't understand this, given that the pip/e-pip/xxx difference (values of 'L') between doubling (or redoubling) and taking is considerably different across these varied methods, right?"
Yes! I see what your getting at. The EPC given by XG indicates a 3.8 diff compared to my estimate, although, according to your estimate, "Penalizing Blue for the open 6-point, the stack on the acepoint and one less checker off makes this more like 45 to 49 which to Kleinman is about 72.5% and an initial double. D+T"
This would be 46-49, wouldn't it? 6 for the ace, 1 for the gap and 1 extra checker makes 8+38, 46-49!
If you meant 7, then you've either taken Ward as the base and worked from there, or you've taken Keith as the base and made a further adjustment in comparison to Ward; Or something along those lines!
My point being, is, the formula works with any of the above, if you get the adjustments right. EPC indicates a 7.2 diff in wastage compared to my 7.5 and your 7/8.
Is your estimate correct? If it is then the Kleinman estimate of 72.5 is way off (see below)!
                     |
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| XGID=-DBDBB-------------bbdbba-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No double | Double/Take |
| Player Winning Chances: | 76.78% (G:0.00% B:0.00%) | 76.69% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 23.22% (G:0.00% B:0.00%) | 23.31% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.536 | +1.068 |
| Cubeful Equities | ||
| No double: | +0.819 (-0.118) | ±0.000 (+0.819..+0.820) |
| Double/Take: | +0.937 | ±0.000 (+0.937..+0.937) |
| Double/Pass: | +1.000 (+0.063) | |
| Best Cube action: Double / Take | ||
| Rollout details | ||
| 165888 Games rolled with Variance Reduction. Moves and cube decisions: 3-ply | ||
| Double Decision confidence: | 100.0% | |
| Take Decision confidence: | 100.0% | |
| Duration: 19 minutes 46 seconds | ||
eXtreme Gammon Version: 2.00.163.beta
Ward+Klienman, (44-49) 0.91, thus 1.1-0.91 according to shaw is worth 76-1.9 = 74.1% (E-Pips 1.81, 75.9) Your estimate of 45-49 is 0.71 72.1 (E-Pips 73.9)
My estimate of 45.5-50 according to Kleinman is 0.79 indicating 1.1-0.79 equiv to 76-3.1 = 72.9 (E-Pips 74.7)
My estimate according to Metric is 77 Your estimate according to Metric is 75.2 (E-Pips 77)
Reviewing XG's estimate of wastage indicates 16.4 (blue) vs. 9.2 (white). Adjusting your estimate to 44.2-49 show a Kleinman ratio of .87, 76-2.3 = 73.7.
Now I am curious!! It would seem that the true value of wastage is pretty much the average between Ward/Keith don't you think?
Just goes to show how sensitive wastage really is, as being out a fraction can make all the difference.
One thing is certain, more work needs to be done!!!
Majestyk