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Path: utzoo!linus!genrad!decvax!harpo!seismo!hao!woods
From: woods@hao.UUCP
Newsgroups: net.math
Subject: Re: Speaking of random numbers....
Message-ID: <548@hao.UUCP>
Date: Thu, 16-Jun-83 13:17:52 EDT
Article-I.D.: hao.548
Posted: Thu Jun 16 13:17:52 1983
Date-Received: Fri, 17-Jun-83 00:35:04 EDT
Lines: 28


   This is in response to the Lance's analysis of the Illinois state lottery.
He points out that:

>   It would seem to me that any time the grand prize was over $1,900,000
>   you would *theoretically* make money by playing. [emphasis mine]

   This is quite true. However, the theory assumes that you can play the game
an arbitrarily large number of times. Yes, you can compute the expected value
(= sum over prizes of [amount of prize * probablility of winning that prize]
-- note that the possibility of winning zero must be included in this sum,
because the definition of expected value requires that the probabilities 
involved must sum to 1.)
that you would win by playing the game once. And, if the number of plays is
large enough, the average winnings per play will indeed approach this figure.
Unfortunately, it is also easy to show that if the probability of winning the
grand prize is p, if you play the game 1/p times, you have a 50% chance of 
not having won the prize yet! Therefore, you may well have to spend millions 
of dollars before your winnings per play begin to approach the expected value.
The expected value is *exactly* what your winnings per play would be if you
could play an infinite number of times. Again unfortunately, none of us can
play an infinite number of times, and only a select few could play the number
of times neccesary to insure approaching this apparently player-favorable
expected value.

                        GREG
 {ucbvax!hplabs | allegra!nbires | decvax!brl-bmd | harpo!seismo | menlo70}
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