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