I'm bored lately and want a non-BG BG problem, and -2, -2 is topical on these forums of late.
Most of the proofs that always doubling is a weakly dominant strategy at -2, -2 rely on the fact that someone will turn the cube as soon as market losers appear. Is it possible that gammons can affect this? E.g., no market losing sequence ever appears, but eventually one side rolls something that lets him become TG or TG/T or some such. It's probably impossible from the initial position, but one can be arbitrarily constructed, I think. Is it problematic for the proof?
For example:
The score (after 0 games) is: White 0, Blue 0 (match to 2 points)
Move number 5: Blue on roll, cube decision?
| White | 270 |
|---|---|
| |
| Blue | 37 |
Position ID: AIC7uwPf94AAAA Match ID: cAlAAAAAAAAA | |
• Blue doubles
| Cube decision | |||
|---|---|---|---|
| 4-ply cubeless MWC | 66.515% | (Money: +0.5429) | |
| 0.5288 0.5196 0.0002 - 0.4712 0.0339 0.0005 | |||
| Cubeful equities: | |||
| 1. | No double | 53.072% | |
| 2. | Double, pass | 68.145% | 15.073% |
| 3. | Double, take | 52.876% | -0.197% |
| Proper cube action: | No double, take (1.3%) | ||
GNU's opinions may be way off in this position, but let's just say for argument's sake that they're right.
Even though Blue wins 53% according to 4-ply and any 6 is a giant market loser, GNU says he should not double. GNU also thinks White on roll should not double, but that seems wrong.