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Re: Enchanted Forest (I and II)
Posted By: gremlinn, on host
Date: Monday, July 8, 2002, at 10:34:33
In Reply To: Re: Enchanted Forest (I and II) posted by gremlinn on Monday, July 8, 2002, at 10:21:29:

> > Obviously this is a pretty highly unlikely occurrence. I'll leave it to you to calculate some estimates on its probability.
> >
> > In any event, the window of opportunity for firing up a repeat game ends after 32768 seconds.
> Hmm, so what'd you need is for exactly 32768-x processes to start up within the x seconds after starting a particular game, for you to get the same layout on the second game (assuming x is less than 32768).

It just occurred to me that 32768-x processes (mod 32768) starting up is a necessary, but not sufficient condition. You also need the process ID number to wrap around the top so that your process ID is exactly x less, which happens with conditional probability 1 - x/32768. So a better approximation of the chance of a repeat random seed for two games would be 1/32768 * (1 - x/32768). For x = 1800 (two games half an hour apart) this is about 1/34672, and it gets slightly less likely as you increase x, the duration between the two game starts. This makes the calculation a little harder, but I don't think it changes my conclusion of the last post.

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