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What "cubeful" equities are and how to compute them

Posted By: Daniel Murphy
Date: Friday, 8 January 2010, at 3:12 p.m.

In Response To: What "cubeful" equities are and how to compute them (Timothy Chow)

GNU reports wins/gammons/backgammons for each side. These mean what you think they mean: double/pass counts as a simple win,

No. I think I wrote this before, lost somewhere in the thread now. When Gnubg, while doing a rollout, ends a trial with double/pass, at that point it evaluates the position. Its evaluation includes estimated wins/gammons/backgammons for each side, if the trial were to continue. For that trial, that range of evaluated wins/gammons/backgammon, not simply a simple win, goes into its report of "cubeless" wins/gammons/backgammons. You can verify this: set up a position where Player Blue on roll has some number to play, after which immediate cube action for Player White is double/pass and Player Blue loses some gammons. Roll out any play of the number. If the rollout really reported double/pass as a single win, it would report White winning 100% single wins. It won't.

Here, an example:

The score (after 0 games) is: White 0, Blue 0

Move number 4: White to play 61

White92


2X2X3X3X3X ' ' ' ' ' '3O

2O2O2O3O3O ' ' ' ' ' ' '

Blue78

Position ID: 2+4ABwDb3QEAYA Match ID: MAEHAAAAAAAA

• White moves bar/19

Cube decision
2-ply cubeless equity -1.0493
0.1079 0.0131 0.0004 - 0.8921 0.2764 0.0023
Cubeful equities:
1.No double -0.9624
2.Double, pass +1.0000 +1.9624
3.Double, take -2.2742 -1.3117
Proper cube action:No double, take (40.1%)

# Ply Move Equity
1 R bar/19 -1.0000
0.15030.01440.0000-0.84970.18570.0027 -0.8734 -1.0000
0.00000.00000.0000-0.00000.00000.0000 0.0000 0.0000
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 846008638 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 0-ply cubeful [expert]

in my opinion, this ["cubeless" equity] figure is misleadingly named (because it is derived from statistics from a live-cube rollout)

Yes and no. Although I do often call it "cubeless" in quotes, because it hasn't been found by doing a cubeless rollout, and I may have said that it's not "really" cubeless, it actually is the cubeless equity, although (a) it hasn't been found by doing a cubeless rollout, rolling out each trial to the end) (b) bot evaluations sometimes make up part of the data that informs the cubeless equity, and (c) the bot isn't playing cubeless money game checker play anyway.

and it is also useless, because what we really care about is the value of the game taking the cube into account.

It's more useful sometimes than other times, but it's not useless. For instance, we can look at cubeless and cubeful equities, looking for fishy bot play, or to better understand cube value in the position.

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