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What "cubeful" equities are and how to compute them

Posted By: Timothy Chow
Date: Friday, 8 January 2010, at 4:07 p.m.

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

I stand corrected about the point that Daniel Murphy made, about what GNU does when it ends a trial with "double/pass." Somehow I thought we had come to a different conclusion at the end of the discussion—my mistake. The implications of this (to me) bizarre behavior are interesting. It means that calling the w/g/bg figures "cubeless" figures is not as bad a misnomer as I thought. Presumably, GNU does this in order to mimic as closely as possible the cubeless figures that people have gotten used to seeing from Snowie. But more importantly, it means that one has to be extra cautious when making (human) inferences such as "Play A leads to more wins but fewer gammons than Play B," because such reasoning often tacitly assumes that a double/pass is a win. I knew that this was a problem with cubeless rollouts but (erroneously) thought that this problem had been fixed in GNU.

I also realized that there is still an open question about what Snowie means by "live-cube equity." There are (at least) two different things it could mean.

A. It could mean what GNU means by "cubeful equity." As I explained, GNU computes this not by using Janowski but by directly averaging over all the trials, taking the cube value and gammons into account (and then, optionally, applying a variance-reduction adjustment).

B. It could mean that it is using Janowski's formula, with the so-called "live-cube model" of cube efficiency.

I think anybody who owns Snowie could help settle this issue by answering these questions:

1. Does Snowie have an option in which the actual value of the cube is tracked throughout each trial game, so that in principle you could get Snowie to output a table like GNU's, in which you see how many games end with the cube value on 2, 4, 8, etc.?

2. Does Snowie report both a "cubeful equity" and a "live-cube" equity when you ask for a cubeless rollout?

If the answer to question 1 is yes, then it seems likely that Definition A of "live cube equity" is correct, at least when this option is turned on. The whole point of tracking the cube value during a trial is to be able to compute equity in this manner.

If the answer to question 2 is yes, then it seems that Snowie has to be using Definition B or something like it, at least in cubeless rollouts, because there isn't any way to make sense of Definition A for a cubeless rollout.

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