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this should be easy.. - ROLLOUT

Posted By: Timothy Chow
Date: Saturday, 28 June 2014, at 12:33 a.m.

In Response To: this should be easy.. - ROLLOUT (Tom Keith)

The following remarks will hopefully also address Bob Koca's question.

What does "cubeless" mean? One possibility is the following:

Definition 1. A "cubeless" probability of winning/losing a single/double/triple game, or a "cubeless" equity, refers to the probability or equity of a position under the assumption that the position is played out by perfect players as if cubes and matches had never been invented.

Another possibility is this:

Definition 2. "Cubeless" means "with no cube."

Definition 2 looks simpler and more intuitive at first, but it's ambiguous. At a score when the cube is live, what does it mean to assess the probability of winning "with no cube"? You can't just remove the cube; you have to define how subsequent play is to proceed. Are the players supposed to play out the rest of the match without a cube, using a cubeless MET? Or do they just play out the rest of the game without a cube, understanding that the cube will be reinstated after the game is over? Or by "with no cube" do you mean "cubeless" in the sense of Definition 1? Given this ambiguity, I think that it's ambiguous what "cubeless" means even at n-away Crawford when n ≥ 3. Does the cube get reinstated after the conclusion of the current game? Even at GS/GG/DMP, Definition 2 strikes me as ambiguous because it could refer to Definition 1. This is especially true if we agree to use Definition 1 except at GS/GG/DMP; it seems pretty confusing to me to use Definition 1 at all scores except GS/GG/DMP and then switch to some other definition of "cubeless" just for those three scores.

The other argument for using Definition 1 is that this is what the bot writers have in mind. When Snowie reported cubeless numbers, it meant Definition 1. In particular, when Snowie reported cubeless numbers at (say) gammon save, it did not mean ATS numbers. Even for modern bots, during a rollout, if there is a D/P that forces the bot to generate an estimated "cubeless" equity, they try their best to come up with an estimate in the sense of Definition 1. Now, it's true that at gammon save (for example), the "cubeless" probability of winning that it ends up computing happens to be the ATS probability of winning, but to me, this is an artifact of the algorithm. The algorithm, in general, isn't trying to compute the ATS probability of winning. It's trying to compute the cubeless probability of winning in the sense of Definition 1, and the fact that at some scores it winds up computing the ATS probability of winning instead is, in my mind, an "accident" of sorts.

Anyway, this is a long-winded explanation of why I prefer Definition 1 of "cubeless" and insist on using "pseudocubeless" to refer to the bot numbers, even at gammon save.

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