On 2017-08-21 16:40, Philippe Michel wrote:
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).
In principle, yes, but as I understand it, eXtreme Gammon doesn't use quasi-random dice and its variance doesn't seem to suffer much. If this is true then I would infer that low-discrepancy sequences won't reduce the variance much.
Something that might have a better chance of yielding superior results is to use 1-ply or even 2-ply for the variance reduction computation instead of 0-ply, at least for the first or second steps of a rollout trial. Obviously this would slow things down but it's conceivable to me that the improved accuracy of the luck estimate might compensate for it, so that fewer rollout trials would be needed to drive down the variance.
Tim _______________________________________________ Bug-gnubg mailing list Bug-gnubg@gnu.org https://lists.gnu.org/mailman/listinfo/bug-gnubg
