A domain where not-nearly-random dice may be useful could be rollouts and
even more so repeated interactive playout of a position.
Currently, rollouts ensure that each sucessive set of 36 trials uses every
possible diceroll once and the 36 rolls' ordering is random. For playing
out positions, there is nothing special available.
The involved math is too hard for me, but wouldn't using low discrepancy
sequences (https://en.wikipedia.org/wiki/Low-discrepancy_sequence) instead
of a random order decrease the variance for rollouts with any number of
trials (possibly only slightly, with variance reduction already helping a
lot). When playing out a position, it could be more effective to sample
the set of possible outcomes this way rather than purely randomly.
Do you have some insights on the subject ?
Do you think it would be indeed useful for rollouts and not too visibly
contrived for a possible interactive usage ?
Then how does one generate such sequences ? Would the methods that are
used on a continuous interval work for a discrete set of 36 values, not
particularly homogeneously spread ? How to generate varied sequences, not
always something identical like "moderately good, very bad, average, etc...) ?
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