Re: [Bug-gnubg] Rotating rolls in rollout

[nis]

--On 04  Oct 2002  09:18 +0000 Joern Thyssen <address@hidden> wrote:

> > What are the implications for rollout reliability and significance if
> > a number if trials is chosen which isn't a multiple of 1296?
>
> I'm not sure.

This is rather important! I have a suggestion - see below.

> > Or if the rollout is interrupted?
>
> If you requested 1296 trials but only performed 36 you would get the
> following dice sequences:
>
> Game 0: 11-11-random...
> Game 1: 21-11-random...
> Game 2: 31-11-random...
> Game 3: 41-11-random...
> Game 4: 51-11-random...
> Game 5: 61-11-random...
> Game 6: 12-11-random...
> ...
> Game35: 66-11-random...

This means that breaking off at this point gives a biased result, as you 
also mentioned. More important, it reduces the value of watching the 
rollout results as they are created ...

> > The order of the rollouts might be important.
> > If the rollout has only rolled out all the 1x rolls, then the rollout
> > could be biased. Perhaps the Variance Reduction eliminates most the
> > bias?
>
> I guess it would remove some of it, but I think it would still be
> biased.

True.

My suggestion would be to scramble the sequence of first rolls, while still 
using each of them one time. This might also allow stratification of 
rollouts which are not a multiple of 36 or 1296, and might be easily 
extendable to

--
Nis Jorgensen
Amsterdam