Why does GNUbg report cubeless numbers as part of the cube decision?
All the bots report game outcomes in this same way. The game outcomes in evaluations and in cubeful rollouts are estimates of how games would turn out if the doubling cube were never used (in a truly cubeless rollout, they are exact, not estimates). As to why, (1) if you wanted to know cubeful game outcomes and they would be useful in some position, you'd probably want to know a lot more detail -- how many single games, gammons, backgammons were won on every cube level (2) cubeful breakdowns in cubeful evaluations or rollouts mimic how we often go about making cube decisions -- first determine cubeless probabilities, and then assess the effect of cube ownership. How bots handle this has been discussed many times in this forum. You could read a particularly critical view of "cubeless" results here:
http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=57713
In your example position, how many different numbers do you want a bot to report? The bot tells you that if the game were played out with no doubling cube, Blue on roll would win 17/36 + 14/36*2/36 + 3/36*2/36*34/46 + 2/36*2/36*31/36 = 50.08%. Do you also (or instead of that) want the bot to tell you that if you don't double you win 47.22% of all games? That if you do double you win 47.22% of all games? What if the position were more complicated -- suppose the cube could get up to 4, or 8?
When a discussion of cubeless/cubeful equities comes up, I often think of the Jacoby Paradox positions that novice players learn --
Move number 8: Blue on roll, cube decision?
| White | 2 |
|---|---|
| |
| Blue | 7 |
Position ID: AwAAEAEAAAAAAA Match ID: UQkAAAAAAAAE | |
-- why this position, where you win 52.77% is a redouble, but this --
| White | 5 |
|---|---|
| |
| Blue | 7 |
Position ID: EQAAEAEAAAAAAA Match ID: UQkAAAAAAAAE | |
-- where you win 61.9% cubeless, is not a redouble, or this --
| White | 4 |
|---|---|
| |
| Blue | 7 |
Position ID: BgAAEAEAAAAAAA Match ID: UQkAAAAAAAAE | |
-- where you win 65.8% cubeless, is not a redouble, either.
So, how do we determine the cubeful probabilities in GNUbg?
Meaning the cubeful game outcomes. Look at the cubeful equity and guess, estimate, or know. In games with probable multiple cube turns, and/or with gammons involved, it's difficult or impossible to get directly from cubeful equity to cubeful game outcomes. However, in your simple position, you can, since there are only two rolls left in this game:
If you don't double, your opponent's equity is 0.0555. So he wins 0.5000 + 0.0555/2 = 52.77% of the time. So you win 47.22% of the time.
If you do double, your opponent's equity is 0.1111 (unless he beavers, then it's twice that). So he wins 0.5000 + 0.1111/4 = 52.77% of the time.