Re: [Bug-gnubg] Confidence intervals from rollouts

[David Montgomery]

From: "Douglas Zare" <address@hidden>
> I have a question about the effectiveness of variance reduction. Two
common
> techniques are to subtract an unbiased estimate of luck, and to cycle
through
> the possible rolls on every 36 rollouts, or every 1296 rollouts. To
estimate
> the standard error, one ignores that the second technique is used. This
ought
> to overestimate the standard error. Has anyone determined how much the
> overestimate is?

It depends on the position, of course.  Let's assume
positions like the openings and responses.

Long ago I did some calculations based on JF rollouts,
which use stratified sampling.  I got a negative result
-- the data said the differences were larger than you
would expect from truly independent random samples,
rather than each rollout using stratified sampling.

>From this I concluded that stratified sampling helps
hardly at all for many common types of positions.

I'd have more confidence in my result if someone
repeated the experiment, however.

---

Ah, you just stipulate to cycling through the opening
ply or two.  JF's and my rollout code actually does more
than this, ensuring both perfectly distributed sampling
of the first two ply, and duplicate dice for subsequent ply
for every game.  That's what I mean by stratified sampling.

This should be slightly better than just distributing
the first ply or two, although to the degree there is
any benefit, the first two play probably captures most
of it.

---

David