Re: [Bug-gnubg] TEST RESULT: Variance Reduction

[Jim Segrave]

On Sat 05 Jul 2003 (19:19 +0000), Joern Thyssen wrote:
> On Mon, Jun 30, 2003 at 11:15:20AM +0100, Ian Shaw wrote
> > 4) Rotating opening rolls I rolled out 7776 times (6 * 36 * 36). Then
> > I wondered how the stratification is affected when it's the opening
> > roll. Will the rollout have done any stratification at all? Should I
> > have done a multiple of 21 * 36 = 756? Will the stratification work if
> > I do?
> 
> I assume you mean 30 * 36?
> 
> Stratification will always work, independently of the number of trials.
> For normal rollouts the stratification will be optimal for rollouts with
> a number of trials proportional to 36, 1296, etc. For example, for a 37
> trial rollout one of the rolls will be grossly over-represented compared
> to any of the other rolls. The same of a 3700 trial rollout, but now the
> effect is obviously smaller. 
> 
> I'm not sure exactly what happens for RAIP. Jim? Nis?

RAIP uses the same stratification and then discards initial
doubles. It will be correct for 30 games, 30 * 36, 30 * 36 * 36, etc. 

I've just been looking at this as part of my implementation of
extending rollouts (I have it working for chequer play but not yet for
cube decisions and I need to add some things so that saving a match
will save the rollout info so that you can extend a rollout of a saved
match. I expect to be commiting later this week.

-- 
Jim Segrave           address@hidden