From: collins@newton.apple.com (Scott Collins)
Date: Mon, 18 Apr 94 16:02:59 PDT
To: cypherpunks@toad.com
Subject: 15 out of 16 times...
Message-ID: <9404182130.AA19221@newton.apple.com>
MIME-Version: 1.0
Content-Type: text/plain


It has been known since before I was born (see the very readable "Lady
Luck, the theory of probability" by Warren Weaver, 1963, Doubleday/Anchor
LoC CC# 63-8759) that the value (i.e., here 'cost') of this game is
infinite.

This is described by a correlary of the law of large numbers wherein
(quoting from Weaver, emphasis his):

  By making the number _N_ of trials large
  enough, you can make as near unity (certainty)
  as you desire the probability that the actual
  number _m_ of successes will _deviate from_ the ex-
  pected number _np_ _by as much as you please_.

Note that, effectively, this law applies _before_ the one that lets you win
an expected number of trials.  This is why the person with the greater
bankroll can win even in the face of sub-optimal 'odds'; why Las Vegas
still exists; why gamblers still go broke; and why they go broke quicker
with the doubling system.

If it is not a question of probability, i.e., both parties _know_ the
commodity will perform in a particular way... then this does not apply. 
However, to the extent that they are uncertain --- it does (in spades).


Scott Collins   | "That's not fair!"                         -- Sarah
                | "You say that so often.  I wonder what your basis
   408.862.0540 |  for comparison is."                 -- Goblin King
................|....................................................
BUSINESS.    fax:974.6094    R254(IL5-2N)    collins@newton.apple.com
Apple Computer, Inc.  5 Infinite Loop, MS 305-2D  Cupertino, CA 95014
.....................................................................
PERSONAL.    408.257.1746       1024:669687       catalyst@netcom.com