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From: no5db@ihuxl.UUCP
Newsgroups: net.math
Subject: Re: Speaking of random numbers....
Message-ID: <392@ihuxl.UUCP>
Date: Wed, 15-Jun-83 08:50:35 EDT
Article-I.D.: ihuxl.392
Posted: Wed Jun 15 08:50:35 1983
Date-Received: Thu, 16-Jun-83 20:32:18 EDT
References: <441@ihuxi.UUCP>
Organization: BTL Naperville, Il.
Lines: 39


	State lotteries! Now theres a topic that interests me.

	I have been analyzing the Illinois state lottery and have come
up with the following data. Every week, six numbers from 1 to 40 are drawn.
To win the grand prize you must choose 6 of 40 numbers correctly, 
probability-wise this is a 1 in 3838380 chance, but you get two guesses 
for a dollar so you have about a1 in 1900000 chance of winning the grand
prize for every dollar you spend. Now in addition to the grand prize, 
if you pick five of the six numbers you win a prize around $1100,
and if you pick 4 of the 6 numbers you win about $30. In addition to
the six numbers drawn, one alternate number is drawn. If no one wins the
grand prize for the week an alternate grand prize is given. To win the
alternate grand prize you must pick 5 of the 6 "real" numbers and 
your sixth number must match the alternate number. I believe this prize
has generally been about $100,000.
	Now comes the tricky part. For a given week, if no one wins
the grand prize, part of the grand prize money is allocated towards the
next weeks' grand prize. This means that the grand prize continues to
get larger until someone wins. The minimum grand prize is $1,000,000
and about 4 weeks ago the grand prize had grown to around $3,600,000.
It would seem to me that any time the grand prize was over $1,900,000
you would theoretically make money by playing. As a matter of fact
for a grand prize of $2,500,000 I estimate that the expected return
on every dollar spent is about one dollar and eighty cents! (Try it
yourself if you don't believe it!)
	All this has been puzzling me for sometime, if you played the
lottery every time the grand prize was over $1,900,000 wouldn't
you *have* to make money in the long run??? I think the fallacy in
my thinking is as follows: To come out ahead you would have to win
the grand prize at least once and unless you spent *alot* of money
your chances of winning the grand prize would be too small to be
significant(??)
	This still leaves room for the possibility of a group of
people playing and splitting any prizes won.
	 I would like to hear comments and/or calculations pertaining
to this. If there is enough interest I will summarize the responses.

					Lance