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XG Technical (Cubeless / Cubeful)

Posted By: Jeremy Bagai
Date: Tuesday, 17 July 2018, at 9:52 p.m.

Hi folks,

I'm starting a project looking at cube actions over a variety of scores and want to make sure I understand what's really going on in XG for at-score decisions.

So here are a series of statements about XG that I *think* are true. I'd appreciate corrections or any informed comments, thanks.

1. XG 1-ply produces a cubeless outcome distribution for a position. There is no built-in notion of cube-equity or cube-efficiency.
2. At 1-ply, that outcome distribution gets transformed into a cubeful-equity by way of Janowski's equation, including some default assumptions about cube efficiency:
   1. That efficiency equals some default value
   2. That efficiency is the same for each player
3. At 1-ply, cubeless outcome distribution and cube efficiency (for each side) are the only inputs used for cubeful equity. Those plus an MET are the only inputs needed for a cubeful equity at score. This means that any two different positions that share the same cubeless outcome distribution and efficiency estimates should also yield the same money and at-score cubeful equities, at least in the eyes of XG. (Is this true in real life?)
4. At some level of analysis (3-ply, +, ++?), not only is the cubeless outcome distribution improved (naturally), but XG is also better able to estimate cube efficiency for each player. (I'm getting this from Rick J, here.) Better estimates of cube efficiency lead to better cubeful-equity estimates, both for money and at score.
   1. Except, by the time you get to ++ XG isn't really just improving its cubeless outcome distribution anymore, is it? It's actually doing some sort of truncated *cubeful* rollout? Help, please.
5. Consider the same position at different scores, analyzed at ++. Will that same position produce different efficiency values at different scores? I expect the answer must be Yes, since different scores have vastly different cube-windows, some of which might allow for no cube efficiency at all. But I'm not actually sure . . .

Thanks for your comments or questions.