Um...blitzxz... this is game 2, not game 1. Please correct the title. Thanks
So we're now at 3-away 5-away. This is where cube handling starts to get interesting....
GnuBG rollout from the team's point of view (the doubling side):
Spoiler
Rollout details:
Centered 1-cube:
65,36 33,32 1,94 - 34,64 6,87 0,46 CL +0,6691 CF +0,8618
[ 0,08 0,17 0,11 - 0,08 0,06 0,05 CL 0,0025 CF 0,0062]
Player factotum owns 2-cube:
66,00 34,47 4,21 - 34,00 6,71 0,93 CL +1,6973 CF +1,2413
[ 0,10 0,23 0,23 - 0,10 0,09 0,10 CL 0,0070 CF 0,0099]
Full cubeful rollout with var.redn.
3888 games, Mersenne Twister dice gen. with seed 819074783 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 6 more moves within equity 0,09
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
Summary:
Cubeless: +0.6691
No double +0.8618 (-0.1382)
Double, pass: +1.0000
Double, take: +1.2413 (+0.2413)
Proper cube action: Double, pass.
Perhaps a quick explanation of all these numbers is in order:
The numbers are all wins (including (back-)gammons), gammons (including backgammons), and backgammons, then the same for opponent.
So we win roughly 2/3 of all games here, and 1/3 of all games will win a gammon for us (that is, half of our wins will be gammons). 1/3 of all games will be won by factotum with a pretty small percentage of gammons for him.
The result is that without a cube in play at all, we'd win about 0.67 points (cubeless equity: CL) on average. If we don't double now, but with a cube in play that we might use later on, we win 0.86 points on average (centered cube, cubeful equity CF); clearly we get value out of the cube (cube vigorish) even if we don't use it right away.
If we double, we either win 1 point if factotum passes, or as the rollout says, 1.24 points on average if factotum takes.
So clearly, we should double (instead of 0.86, we win at least a full point, more if factotum takes). Even clearer, factotum should pass, so he loses just 1 point instead of an expected 1.24 if he takes.
The figures in square brackets [ ] are the statistical errors that could be present in the rollout, as it is just a sample of possible outcomes. There's a lot to say about that but I won't do it here. Suffice to say these figures should be as low as possible; in this rollout they're quite small so it has strong (statistical) significance.
Bottom line: not doubling would be a 0.14 whopper with cheese for the team; not passing would be a 0.24 double whopper with extra onions for factotum.