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Re: [Bug-gnubg] What's quasi-random dice?

From: Joern Thyssen
Subject: Re: [Bug-gnubg] What's quasi-random dice?
Date: Sat, 14 Jun 2003 13:13:58 +0000
User-agent: Mutt/1.4.1i

On Sat, Jun 14, 2003 at 07:55:58AM -0400, address@hidden wrote
> Hi
> What's quasi-random dice 

Quasi-Random Dice are used to reduce the element of luck in rollouts.
Instead of selecting purely random dice, gnubg will ensure a uniform
distribution of the first roll of the rollout.  If 36 trials is
requested, one game will start with 11, two games with 21, two games
with 31, etc. In general, if n * 36 games is requested, n games will
start with 11, 2*n games with 21 etc. This is called _rotation_ of the
first roll. Similarly, if n*1296 trials is requested, the second roll
will be rotated, such that n games will start with 11-11, 2*n games
with 11-21, 4*n games with 21-21, etc. The third roll be also be
rotated if the number of trials is proportional to 46656.

Suppose a user stops a 1296 trial rollout after 36 games. The 36 games
would have had the following rolls for the first two rolls of each
game: 11-11, 21-11, 12-11, 31-11, 13-11, ..., 66-11 Obviously such a
rollout will give skewed results since the second roll was 11 for all
games! To avoid this problem gnubg will randomise the sequence of rolls
such that it is guaranteed that for any sample of 36 games you have
exactly one game with first roll 11, exactly one game with second roll
11, etc. This is called _stratification_.

gnubg will actually also rotate and stratify rollouts where the number
of trials are not multiples of 36, 1296, etc. The distribution of rolls
is obviously not uniform any longer in this case, but it will still
provide some reduction of the luck, i.e., no 37 trial rollout will have
3 games with a initial 66.

(Nis or others: please correct me if the above is wrong!)

> and when should I use it?



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