Neil:That cubeless equity is based on evaluation?
It has to be, in a cubeful rollout with cube action. When there's a double/pass, the trial ends, and Gnubg evaluates the position. That evaluation helps make up the "cubeless" equity and game breakdown.
Here's a good example:
Money Game. Jacoby Rule. Blue on roll.
| Cappucino | 26 |
|---|---|
| |
| Latte | 115 |
Position ID: 7hQAALZtAwCwAA Match ID: cAkAAAAAAAAA | |
Alert: wrong double ( -0.2006)! [very bad]
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.0229 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.3889 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.0000 | +0.6111 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.1883 | -0.2006 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No double, take (24.7%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 324 games, Mersenne Twister dice gen. with seed 868851875 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] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Check out the "centered 1-cube" line. With Jacoby Rule on, if Blue doesn't double now, either Blue will hit and double White out, or Blue will miss and White will double Blue out. The cubeful equity 0.3889 is spot on. Blue wins 25/36 = 69.44%, so Blue's cubeful equity is 11/36 = 0.3888. For this cubeful position, that cubeful equity is the only meaningful number in the "centered 1-cube" line.
How does Gnubg come up with Blue winning 63% "cubeless" and "cubeless" equity of 0.0229? In the 69.44% of trials that end when Blue doubles White out, Gnubg estimates that Blue's winning chances are about 83%. That's way off, since Blue should win about 91% after a single hit, and about 95% of the time after an immediate double hit. When White doubles Blue out, Gnubg estimates that Blue's winning chances are about 16%, and that's about right. All together, Gnubg estimates that Blue wins 63.02% of the time, and that's way off. Truly cubeless, Blue should win about 68% of the time.