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## Re: [Bug-gnubg] Confidence intervals from rollouts

 From: Douglas Zare Subject: Re: [Bug-gnubg] Confidence intervals from rollouts Date: Thu, 5 Sep 2002 22:13:56 -0400 User-agent: Internet Messaging Program (IMP) 3.1

```Quoting Joern Thyssen <address@hidden>:

> On Tue, Sep 03, 2002 at 12:53:21AM -0400, Douglas Zare wrote
> > There was an interesting question on the Gammonline bulletin board about
> the
> > standard deviation in cubeless rollouts and the standard deviations of live
>
> > cube results. I've included an excerpt below, in which I attempt to
> estimate a
> > confidence interval for the difference between doubling and not doubling.
> I'm
> > not sure what the best way to do this is, but I suggest that an attempt
> would
> > be worth implementing in gnu.
>
> I'm sorry but can you explain further :-)
>
> A lot of the text below concerns the fact the Snowie doesn't calculate
> the standard error of the cubeful equity, however, gnubg does.

Snowie does provide a confidence interval for the live cube rollouts, but not
the adjustments of cubeless rollouts. Anyway, the question is what is required
to be able to conclude that doubling is better than not doubling (at least for
your rollout parameters). You could wait until the confidence intervals for
doubling and not doubling do not overlap. Even before then, if the rollouts
were independent, you could stop when the two were separated by enough joint
standard deviations. However, if you use a single cubeless rollout to estimate
both numbers, then the numbers are highly correlated. That way you can have a
higher confidence that doubling is correct, even if you don't yet know that not
doubling has an equity less than A which is less than the equity from doubling.

Geometrically, after a rollout, you might have a density on the x-y plane of
possible real equities after doubling (x) and not doubling (y). There might be
an ellipse, analogous to the confidence interval, which is stretched in the
direction of the y=x line, i.e., the projection to the x-axis is large, and the
projection to the y-axis is large, but the projection to the line y+x=0 is
small. You might know that y-x = 0.1 +- 0.03, while you only know that y=0.8+-
0.15 and x=0.7+-0.15.

By the way, I should have indicated more clearly that everything after the
first paragraph in that excerpt was mine.

Douglas Zare

```