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21$.21 ??

Posted By: Ian Shaw
Date: Thursday, 15 November 2007, at 1:28 p.m.

In Response To: 21$.21 ?? (Stick)

I have firmly come to believe that GNU underestimates its own variance (as does Snowie)

I believe the opposite. Gnubg's variance reduction routine assumes that the dice are random. In fact, they are not. Gnubg rotates its rolls in sequence so that there is an even distribution of rolls. After 46656 trails, each possible sequence will have occurred exactly once. (The sequence is pseudo-randomized so that results are not distorted if the number of trials is not a multiple of 36.)

Therefore, since it is impossible for every roll in the trial to be 66 (for example), the actual variance must be lower than the calculated variance.

On what basis do you hold your opinion?

Messages In This Thread

• 21$.21 ??
  RobertFontaine -- Thursday, 15 November 2007, at 4:48 a.m.
  • 21$.21 ??
    Stick -- Thursday, 15 November 2007, at 11:33 a.m.
    • 21$.21 ??
      Ian Shaw -- Thursday, 15 November 2007, at 1:28 p.m.
      • 21$.21 ??
        Stick -- Thursday, 15 November 2007, at 7:12 p.m.
  • 21$.21 ??
    Ian Shaw -- Thursday, 15 November 2007, at 11:34 a.m.