BGonline.org Forums

Consistency of 1st, 2nd, 3rd move rollouts

Posted By: Timothy Chow
Date: Friday, 27 November 2009, at 3:23 a.m.

One of David Rockwell's comments reminded me of a question I've had for some time regarding opening-move rollouts. If you take the equity estimates from 2nd-move rollouts, and average them in the obvious way to obtain equity estimates for the 1st move, how close are these numbers to the equity estimates obtained directly from 1st-move rollouts?

In case that wasn't clear, here's a rephrasing of the question. There are two ways I can obtain equity estimates for, say, an opening 21$. One way is to roll the thing out directly. The other way is to take the twenty-one possible 2nd moves following a 21$, do twenty-one separate rollouts, and then mathematically average these twenty-one equities to deduce the equity of 21$. In a perfect world, these two methods would give exactly the same answer. How close are the two answers in the real world?

We can ask the same question for the 2nd/3rd roll instead of the 1st/2nd roll.

I gather from David Rockwell's remarks that we don't get quite the same answers because (for example) GNU 2-ply doesn't always choose the play that a GNU rollout prefers. What I'm wondering is how big the discrepancy is.

In principle I could answer this question myself for the 1st/2nd roll (at least for money and DMP) using Stick's posted rollouts, but if someone else has already done this then I figure I would save myself the trouble.