GNU Backgammon

 Quasi-random dice in rollouts

 From: Ian Shaw Address: ian.shaw@iee.org Date: 3 March 2004 Subject: Re: gnubg quasi-random dice Forum: GammOnLine

```Here is Joern's explanation from the gnubg archives.

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.
```

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Personal reflections  (Louis Nardy Pillards, Sept 2002)
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Quasi-random dice in rollouts  (Ian Shaw, Mar 2004)
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