Re: variance reduction [Was Re: [Bug-gnubg] Measuring performance levels]

[Douglas Zare]

Quoting address@hidden:

> On 24 Oct 2002 at 18:31, Joern Thyssen wrote:
> 
> > Sorry, I meant: "... since it requires 21 n-1 ply evaluations". 
> > 
> > BTW, is this actually necesary: we just want an estimate of the luck of
> > the given roll. Would it be sufficient to do a 0-ply evaluation of the
> > luck, or would that introduce bias?
> 
> A 0-ply variance reduction should be fine - it will of course be less 
> effective than a 2-ply, but also very much faster. The entire point 
> is that you can add anything which averages to 0.
> 
> I don't remember the context where Douglas asked for 2-ply VR - 
> perhaps there was a reason?

Yes, the reason was that I asked about a 4-ply rollout. The extra time from 2-
ply rather than 0-ply variance reduction is negligible compared with the time 
to evaluate the plays, and it might greatly increase the effectiveness of hte 
variance reduction. Actually, it might make more sense to use 2-ply variance 
reduction on one side and either 1-ply or 3-ply on the other side of that 
position.

There are different things that one might call 2-ply variance reduction. The 
value for a roll comes from the best play with that roll. One can use 0-ply to 
select that play, or 2-ply, or the one that is alphabetically first. Then one 
evaluates that play, possibly using a different ply than what selected the move.

Douglas Zare