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Play A "loses more gammons"

Posted By: Timothy Chow
Date: Monday, 18 January 2010, at 6:54 p.m.

In Response To: Play A "loses more gammons" (Matt Ryder)

Matt Ryder wrote:

Are you saying that the bot rolls out a branching decision tree for the cube and every possible future cube which may occur before its truncation point?

No, certainly not. What I'm saying is this. If you ask GNU to roll out a cube decision for you, it will do two rollouts in parallel. The first rollout is the "no double" rollout, in which the cube is not turned right away, and the second rollout is the "double, take" rollout, in which the cube is offered and accepted. These are labeled something like "Player gnubg owns 2-cube" and "Player tchow owns 4-cube" respectively (assuming that gnubg currently owns the 2-cube and we're wondering if gnubg should redouble and if tchow should take).

During each trial of the rollout, GNU keeps track of the cube, and then terminates either when one side bears everything off, or the trial ends in double/drop. Now, for the purposes of reporting the "cubeless" numbers, GNU will do an evaluation to estimate how many w/g/bg would result if the trial had not been truncated. (Variance reduction might enter here; I'm not sure and will ignore that.) This is what I think you're familiar with.

But the other thing that GNU does, which you can see if you "View Statistics," is to keep track of how many trials end with various outcomes: win with the cube on 2, gammon with the cube on 2, loss with the cube on 4, etc. It keeps track of this for both the "no double" rollout and for the "double, take" rollout.

So if you want to know how many gammons you'll win if you take, then you can "View Statistics," click on the tab saying "Player tchow owns 4-cube," and look at the "gammons" column.

Given that we're doing a rollout, it is these "View Statistics" numbers that GNU uses to compute the cubeful equities of "no double" and "double, take" (again, ignoring variance reduction). Given that this is how GNU is doing the computation, it strikes me that we may be better off looking at these numbers than at the cubeless numbers (which GNU is reporting to you but not using for its internal computation).

Now Daniel Murphy and Bob Koca seem to be trying to convince me that the cubeless numbers are a better way for humans to understand a position. I'm not yet convinced, especially when it comes to understanding recube vig, but we're still debating that. However, I don't think that they disagree with me that this is how GNU does things; it's a question of whether humans are better off "Viewing Statistics" or viewing cubeless numbers.

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