Match 1, Game 2, Move 5, factotum cube

[blitzxz]

Take or pass?

Score:
Black(forum) 1, White 0, match to 5

Pip:
Black 135 White 149

GnuID:
4HPKAwjGnoMBKA:cBGgAAAACAAA

[factotum]

Pass.

[ah_clem]

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....

[Zorba]

GnuBG rollout from the team's point of view (the doubling side):

(click to show/hide)

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.