When you do a cubeful rollout with a bot, it reports the cubeful equity but it also reports the w/g/bg (win, gammon, backgammon) numbers for each side. But usually one thinks of those as cubeless numbers. In a cubeful rollout, some games (maybe even all games) will end with a double/pass, so what do w/g/bg numbers mean in that case?

Consider the following position, where the exact cubeful equity can be easily calculated:


Here, if Black rolls a 6, then (on the next roll) Black will double and White will pass. If Black does not roll a 6, then White will double and Black will pass. So the cubeful equity is 11/36 - 25/36 = -14/36 which is about -0.389.

Note that in this position, *all* sequences lead to a double/pass by one side or the other. No games are played to completion.

I rolled this out in both XG and GnuBG. As expected, they both report the correct cubeful equity of -0.389. So the cubeful rollout is being done correctly.

However, both programs also report some w/g/bg numbers. Both report around 34.5% win (for Black) with some very small percentage of gammons for both sides. Where do these numbers come from? How can there be gammons when all sequences end in double/pass? The fact that both bots report around 34.5% is interesting. It suggests this number is somehow coming from a similar process in both bots, though I cannot figure out how 34.5% is related to this position. The obvious number, the probability of rolling a 6, is 11/36 = 30.6% so that's not it. And it seems unlikely to be the cubeless probability of winning (and even if it was, the rollout stopped at the double/pass so how could it get this number?)

Edit: I rolled this out at DMP on GnuBG and it seems that this 34.5% is the cubeless probability of winning. But this rollout took around 40 seconds while the original cubeful rollout was instantaneous (as expected, since there was an immediate double/pass by both sides). So how these numbers were obtained is still a mystery to me.

The numbers are the probability of wins, gammons, and backgammons if the game were played to a conclusion without a cube in play.

But how is it calculating those numbers from the rollout, if the game was terminated early due to a double/pass? And it is being terminated early, because the rollout at DMP takes a lot longer than at money play.

Thinking about it some more, I suppose it could be that at the point of the double/pass, it just applies the neural net's cubeless estimate of the w/g/bg.

Correct. The information is useful even if it's not the result of a rollout.