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From: bhayes@glacier.ARPA (Barry Hayes)
Newsgroups: net.puzzle
Subject: Re: random number wanted between neg inf and pos inf
Message-ID: <2492@glacier.ARPA>
Date: Mon, 16-Dec-85 22:33:22 EST
Article-I.D.: glacier.2492
Posted: Mon Dec 16 22:33:22 1985
Date-Received: Wed, 18-Dec-85 05:32:00 EST
References: <33@decwrl.UUCP>
Reply-To: bhayes@glacier.UUCP (Barry Hayes)
Organization: Stanford University, IC Laboratory
Lines: 34

It may not make sense to talk about "choosing randomly" one of
an infinite number of possibilities.  Just watch...

Let's play a game.  I have, in this large and ornate paper bag,
an infinite number of poker chips.  Each poker chip has one integer
on each side, and, in fact, the two integers on any poker chip
differ by exactly one.  The game is played as follows:

1) I reach into the bag, and choose a random poker chip, without
   peeking at the chip.
2) I hold it between us so that I can see one side, and you can see
   the other, but neither of us sees both sides.
3) Either of us can reject the chip, just from seeing the side we see.
4) We bet some fixed amount.
5) The person with the low side wins.

The distribution of the chips is as follows:
Chip numbers     how many
1/2              1
2/3              2
3/4              4
4/5              8
and so on

I calculate the odds as follows:
If I see "1" on my chip [a very unlikely event] I must win.
For any other number [say "4"] there are twice as many chips which
will win for me [8 "4/5" chips] as will lose [4 "3/4" chips].  Therefore,
I should always bet, and I will win 2/3 of the time.

You of course can make the same calculations and will also win 2/3
of the time.

 -Barry "at no time do my fingers leave my hands" Hayes
  bhayes@glacier