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15 out of 16 times...



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
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