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 ................|.................................................... 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
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.
Actually, the casinos win in Las Vegas because the odds of almost every bet are in their favor. (Occasionally some blackjack bets are good for the customer. I believe that's the only exception.) Larger capital allows you to affect the distribution of winnings, but not whether or not the underlying bet is a good one. Employment of this strategy means most outcomes will be slightly positive with a small chance of a loss. The loss will be large. Every casino, in effect, takes on the whole world. As all the bets are independent, it doesn't matter if they are played by one player or by a new player every time. The world has much more capital. Yet the casinos consistently win.
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).
There is a way in which the futures markets can be used for quietly and inexpensively transferring money, even if you can't predict future prices. Let's say a second payment channel exists. However, it is expensive in terms of cost, privacy, or hassle. It also has the property that the cost of transferring $10,000 is the same as transferring $100,000. Most of the time, when you play the futures markets you can get some amount of money to transfer. Once in awhile it doesn't work, so you use the second, expensive, payment channel. Peter
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