Well done, Sean. Like you, I was able to achieve x = 10, but not x = 11. The key is to go beyond gammon overage, into bg overage, but there doesn't seem to be enough overage left in that point from 11 to 12 (4-cube bg).
While our positions do not use snakes, inevitably there is still some containment XG misplay at 3-ply. Here is a rollout of your position at 4-ply:
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| XGID=-eAAAA-A----------bbbbb---:1:1:1:00:0:0:0:10:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 60.12% (G:39.56% B:29.84%) | 59.88% (G:39.50% B:32.45%) |
| Opponent Winning Chances: | 39.88% (G:0.00% B:0.00%) | 40.12% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.939 | +1.446 |
| Cubeful Equities | ||
| No redouble: | +0.996 | ±0.005 (+0.992..+1.001) |
| Redouble/Take: | +0.944 (-0.052) | ±0.012 (+0.932..+0.956) |
| Redouble/Pass: | +1.000 (+0.004) | |
| Best Cube action: No redouble / Take | ||
| Percentage of wrong pass needed to make the double decision right: 48.3% | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 71778669 Moves and cube decisions: 4-ply | ||
| Double Decision confidence: | 92.2% | |
| Take Decision confidence: | 100.0% | |
| Duration: 1 hour 39 minutes | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Note that your position does not quite fall into the window at 4-ply (well, 92% that it doesn't). And chances are, based on short tests that I've run, that the window is kicked still lower (a bit) at 5-ply. However, your window is (a) not inverted (i.e., the NR number is higher than the R number), and (b) nice and wide (.052).
That means that it should be a trivial matter to tweak your position to make it fall into the higher-ply window. Changing Blue's position might be too radical, but weakening White's offense a little should do the trick; e.g., displace one of White's 7pt checkers. I'm not suggesting that you (or I) actually bother to do it, I'm just expressing confidence that it can be done: as far as I'm concerned, you've solved the problem already.
I created a bunch of (x = 10) positions that have a certain window at 3-ply, a lower window at 4-ply, and a little lower window at 5-ply. (The 5-ply tests were hard to pin down, a lot of CPU time spent on too few trials -- high variance. But there was a consistency in direction.) In other words, I had to aim high (above 1.0) at 3-ply in order to find the right window at 4-ply (and hopefully 5-ply).
In order to diminish the effect of lower-ply misplay, I gave White her ace point. Unfortunately, that fix also seemed to narrow the window. Here is a position that works at 4-ply:
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| XGID=-aaaaaC-----a-a----bbb--b-:1:1:1:00:0:0:0:10:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 62.35% (G:37.70% B:30.61%) | 61.47% (G:36.98% B:31.51%) |
| Opponent Winning Chances: | 37.65% (G:0.00% B:0.00%) | 38.53% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.972 | +1.454 |
| Cubeful Equities | ||
| No redouble: | +1.019 | ±0.009 (+1.010..+1.028) |
| Redouble/Take: | +0.987 (-0.031) | ±0.019 (+0.968..+1.006) |
| Redouble/Pass: | +1.000 (-0.019) | |
| Best Cube action: No redouble / Take | ||
| Rollout details | ||
| 5184 Games rolled with Variance Reduction. Dice Seed: 46851906 Moves and cube decisions: 4-ply | ||
| Double Decision confidence: | 99.8% | |
| Take Decision confidence: | 90.3% | |
| Duration: 7 hours 43 minutes | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
As you can see, my window, though it does straddle 1.0, is only .031 wide (though still with ci's of +.019 and +.012). That doesn't promise enough latitude in finding a position that works with x = 11. To get an idea, I rolled out (5k) this position at –11–11, and the equities were 1.007 and 1.075. That they exceed 1.0 is okay (that's just a matter of tweaking). The problem is that the window has become substantially inverted (the same problem you no doubt encountered when trying x = 11).
I encountered a ray of hope when rolling out this same (x = 10) position at 5-ply:
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| XGID=-aaaaaC---a----a---bbb--b-:1:1:1:00:0:0:0:10:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in Rollout | No redouble | Redouble/Take |
| Player Winning Chances: | 62.13% (G:37.32% B:29.96%) | 60.59% (G:36.31% B:31.42%) |
| Opponent Winning Chances: | 37.87% (G:0.00% B:0.00%) | 39.41% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.957 | +1.403 |
| Cubeful Equities | ||
| No redouble: | +1.007 | ±0.037 (+0.969..+1.044) |
| Redouble/Take: | +0.912 (-0.094) | ±0.088 (+0.824..+1.000) |
| Redouble/Pass: | +1.000 (-0.007) | |
| Best Cube action: No redouble / Take | ||
| Rollout details | ||
| 330 Games rolled with Variance Reduction. Dice Seed: 58068548 Moves and cube decisions: 5-ply | ||
| Double Decision confidence: | 63.4% | |
| Take Decision confidence: | 97.5% | |
| Duration: 3 hours 31 minutes | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Now the window is much wider (.094)! The confidence intervals are +.037 and +.088, though. I'm going to extend this 5-ply rollout to see what happens. If the window stays about this wide (or wider), that will encourage me to look for an x = 11 position.
Nack