Re: [Bug-gnubg] Re: rollout settings

[Nis Jorgensen]

Just realized I sent this to Gordon only. Anyway, I will reply 
myself:

On 29 Oct 2002 at 21:34, I wrote to Gordon Bower <address@hidden 
wrote:

> On 29 Oct 2002 at 11:02, Gordon Bower wrote:
> 
> > > There has been some discussion about what happens if you do a rollout of =
> > > < 1296 trials with rotation enabled. If the rolls are not random, you =
> > > might skew the results if you do less than 1296 trials because, for =
> > > example, you miss all sequences where X rolls 66.
> > 
> > At risk of asking something obvious....
> > 
> > Why do we do rollouts in multiples of 36/1296?
> > 
> > Can't we gain a huge savings in how long deep-ply rollouts take, if we
> > do
> > them by powers of 21, and weight each result in proportion to
> > 2^(non-doublets rolled in this dice sequence?) It's only a tiny increase
> > in the complexity of the mean and variance calculations, in exchange for
> > making each ply take only 1/3 as many rolls.
> 
> I have thought almost the same thing ... only we cannot weigh them by 
> just 2^non-doublets, since this depends on the lenth of the game.
> 
> Please note: The _evaluations_ already look at 21 rolls per ply - it 
> is the stratification (=rotation of rolls) for the rollouts that 
> could be helped this way.
>  
> Also note that there is no guarantee that this will increase rollout 
> accuracy (for the same computing time).

I just did some quick calculations which confirmed my hunch: This 
will probably produce worse rollouts (higher standard error for the 
same number of trials). More general: 

If you want to do stratified sampling of a population, the best 
precision of the overall result is achieved if each stratum has the 
same weight in the sample as in the population (unless you have 
reason to assume that the strata have different variance)
-- 
Nis Jorgensen
Friends Development & Support
Greenpeace 
+31 (20) 52 36 202