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What "cubeful" equities are and how to compute them

Posted By: Matt Ryder
Date: Saturday, 9 January 2010, at 7:10 a.m.

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

Hi Tim,

In my opinion... ["cubeless equity"] ...is misleadingly named (because it is derived from statistics from a live-cube rollout) and it is also useless, because what we really care about is the value of the game taking the cube into account.

While I appreciate your efforts in collating complex information from a tangle of separate threads, I feel you're misevaluating the crucial importance of cubeless equity in all of this.

Upon doing its "live-cube" rollout, the bot needs to play out a set of games. This inevitably involves a series of evaluations at every point, each of which involves figuring out both the cubeless and cubeful equity.

This is really no different to what human beings do on each roll. Whenever we're given a cube, we need to first work out the number of backgammons/gammons/wins we'd give up assuming no cube and the game was played to its conclusion. That is analogous to calculating a cubeless equity. Then we factor in the impact of the cube (how cube ownership would vary the number of wins, how much we'd lose if we dropped right now, what would happen if we gave the cube back in future etc.) That's cubeful equity.

The cubeless equity information is therefore not at all "useless"; quite the opposite! Oftentimes a cubeful equity will equal -1 (a drop), which is rather unilluminating - until we look closer at the cubeless probabilities to see why.

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