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Cubeful equities: cube efficiency variable

Posted By: Matt Ryder
Date: Wednesday, 6 January 2010, at 6:15 a.m.

From the GNU manual:

"11.5.5.1 Basic formula for cubeful equities
The basic formula for cubeful equities as derived by Janowski is

E(cubeful) = E(dead) * (1-x) + E(live) * x,

where E(dead) is the dead cube equity (cubeless equity) calculated from the standard formula. E(live) is the cubeful equity assuming a fully live cube. We’ll return to that in the next section. x is the cube efficiency. x=0 gives E(cubeful)=E(dead) as one extreme and x=1 gives E(cubeful)=E(live) as the other extreme. In reality x is somewhere in between, which typical values around 0.6 - 0.8."

(My italicised emphasis.)

Cube efficiency (x) is an important parameter in calculating cubeful equity, but it turns out GNU has a rather simple methodology for varying it. The bot apparently assumes the variable should be in the range 0.6 and 0.7, and applies it to a position as per the following table:

Two-sided (exact) bearoff:n/a
One-sided bearoff:0.6
Crashed:0.68
Contact:0.68
Race:linear interpolation between 0.6 and 0.7

So for the most part it is applied as a uniform 0.68 - until the very late game!

The GNU manual admits:

"There is obviously room for improvements. For example, holding games should intuitively have a lower cube efficiency, since it’s very difficult to double effectively: either it’s not good enough or you’ve lost the market by a mile after rolling a high double or hitting a single shot. Similarly, backgames will often have a low cube efficiency, whereas blitzes have may have a higher cube efficiency."

How does XG deal with this? Is it any more sophisticated? I must admit my faith in the precision of 'cubeful' equity has been somewhat shattered by my investigations so far.