Blue will drop the recube to 8 after his six missing numbers, leaving him with 50% mwc. On his other losses, which number 27/36 * 5/36, he loses the match. So his average mwc when he doubles and loses works out to 30.8%. If he doesn't double and loses, he'll lead -4:-6 for 64.3% mwc (R-K MET). So doubling risks about 34.5 to gain 12.5. Blue's last-roll doubling window opens at 72.8%.
If you work out Blue's actual winning chances after doubling, they come to 72.9%. So this is enough, right? Well, not quite. All of Blue's market losers leave him gin next turn, but if he doubles he will lose a handful of games he would have won had he held the cube. In 6/36 * 31/36 games, Blue wins 1/6 of the time by rolling a set, but only if he hasn't doubled. That's 31/1296, or 2.4% of all games. These games swing 37.5% mwc, as Blue wins two points instead of losing four. This comes to 0.9% mwc overall, and that's enough to swing the cube decision when Blue is so close to the bottom of the doubling window.
Using the W-H MET gives an error of around .07 for doubling, and somebody at the tournament put it in XG and got an error of .1. I don't know what MET they were using.
In the actual match I was White, and happily took the 4-cube. At the time I thought the redouble was a bigger error than it turned out to be. Blue very efficiently rolled 41, and I failed to roll a set after my rewhip to 8. Time to rebuy (again).
The score is: paleface 1, avatar 5 (match to 9 points)
avatar on roll, cube decision?
| paleface | 5 |
|---|---|
| |
| avatar | 7 |
Position ID: DQAAcAQAAAAAAA Match ID: UQkgARAAKAAA | |
• avatar doubles
Alert: wrong double ( -0.046)!
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.506 | (Money: +0.506) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.506 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.000 | +0.494 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.460 | -0.046 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No redouble, take (8.6%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 108 games, Mersenne Twister dice gen. with seed 892247705 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0.16 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skip pruning for 1-ply moves. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||