RE: [Bug-gnubg] Rotating rolls in rollout

[Nis Jorgensen]

--On 04  Oct 2002  11:17 +0100 Ian Shaw <address@hidden> wrote:

> > From: address@hidden [mailto:address@hidden
> > Sent: 04 October 2002 10:48
> >
> > 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
> This might be a good solution. Are you suggesting a static but scrambled
> order, or a random order each time but checking you haven't used that
> permutation before. The latter seems more natural but is probably more
> processor intensive. I suppose you could generate a random sequence
> 1-1296 at the start of the rollout and use it to index through the roll
> permutations.

This is exactly what I was thinking of. I am still trying to find out 
whether this can easily be extended to ensure:

1. Stratified distribution of first rolls in any sequence of 36 rolls.
2. Stratified distribution of n'th rolls when doing at least 36^n rollouts.
(how many people actually do rollouts with 36^3 trials?)

Perhaps something like this (pseudocode)

RollUsed(TrialNumber,Rollnumber) =
        Sum for k = 0 to (Rollnumber - 1)
                of
        ((Trialnumber div (36^k)) mod 36)
                mod 36

I will try looking at the current code, and give my suggestions

> One final query is, what happens to the Standard Error? Zare suggests
> that the SE reported is too high because the variance is reduced by the
> stratification. Is this taken into account? Is it even possible to do so?

The standard error should be too high - although the only person who 
actually reported checking this (in JF) reported that it was too low ... 
but I don't think we have any way of quantifying this in the rollout 
calculations. At the moment let's just be happy if we produce better 
rollouts :-)

--
Nis Jorgensen
Greenpeace
Amsterdam