Two Plus Two Poker Forums What do the w/g/bg numbers mean in a cubeful rollout?
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 12-30-2017, 08:20 PM #1 grape5 stranger   Join Date: Dec 2017 Posts: 9 What do the w/g/bg numbers mean in a cubeful rollout? 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: White - Pips 65 Black - Pips 77 Black on roll. Cube action? Created with www.BGdiagram.com 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. Last edited by grape5; 12-30-2017 at 08:30 PM.
 12-30-2017, 10:10 PM #2 Robertie old hand   Join Date: May 2004 Posts: 1,692 Re: What do the w/g/bg numbers mean in a cubeful rollout? The numbers are the probability of wins, gammons, and backgammons if the game were played to a conclusion without a cube in play.
 12-30-2017, 10:41 PM #3 grape5 stranger   Join Date: Dec 2017 Posts: 9 Re: What do the w/g/bg numbers mean in a cubeful rollout? 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.
 12-31-2017, 11:30 AM #4 Robertie old hand   Join Date: May 2004 Posts: 1,692 Re: What do the w/g/bg numbers mean in a cubeful rollout? Correct. The information is useful even if it's not the result of a rollout.

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