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From: ram@zedat.fu-berlin.de (Stefan Ram)
Newsgroups: comp.misc
Subject: Re: high-school presentation, suggestions?
Date: 21 Mar 2024 21:08:49 GMT
Organization: Stefan Ram
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Johanne Fairchild <jfairchild@tudado.org> wrote or quoted:
>I asked myself---why does the shuffling make the game likely to end? 

  Periodicity (getting into a loop) often is not stable. When you
  start at noon and repeatedly add 12 hours, then you get the
  repeating sequence "noon - midnight - noon - midnight - ...".
  But if instead you add 12 hours plus a random time (even a small
  one), the outcome nearly always will not be periodic anymore.

  Now, imagine that there is some "end rule". For example,
  the addition stops, once a time between 1 p.m. and 2 p.m. is
  reached. With the periodic sequence "noon - midnight - noon -
  midnight - ..." this end interval will /never/ be reached.
  But when a random time is added, it should often be reached.