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RE: [Bug-gnubg] Rotating rolls in rollout

From: Nis Jorgensen
Subject: RE: [Bug-gnubg] Rotating rolls in rollout
Date: Fri, 04 Oct 2002 13:23:10 +0200

--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

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)
        ((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

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