From: John Conover <john@email.johncon.com>
Subject: Re: Stock Market - A Zero Sum game or not?
Date: 25 Jan 1999 02:00:54 -0000
William F. Hummel writes:
> P.S.
>
> I didn't mean to imply the gambler's ruin theorem requires a
> negative expectation in the game. It is meant to show that even
> in a fair game, the house is sure to beat the player if the house
> has effectively an unlimited amount of money to commit.
>
For those that don't know about the gambler's ruin, suppose a gambler
has K dollars, and the casino has B dollars. The chances that the
gambler will go broke, in a fair coin tossing game, before the bank
goes broke is 1 - (K/B). The duration, of average, of the game before
the gambler goes broke is K(B - K) tosses of the coin.
Gambler's ruin has significance in other areas of economics, since the
gamblers capital, over time, is a random walk fractal, and has
characteristics similar to equity and currency values, GDPs,
industrial markets, etc.
John
BTW, William is right-the gambler's ruin shows that even with a fair
coin, the casino is an unfair place to gamble. If the gambler has a
thousand dollars, and the casino a million, the chances of ultimate
ruin for the gambler is 99.9%. Now suppose a small company has 0.1%
market share-it is the same problem-what is its chances of becoming
dominant? 0.1%. Further suppose that that there are a thousand
companies in the market, what are the chances that at least one will
supplant the dominant company eventually? 63.2%. You can work through
the numbers to get some insight into the peculiar problem that an
oligopoly is not significantly better than a monopoly as far as moving
new concepts and ideas into the marketplace. A panoply is
significantly more successful at that. But much more risky for the
investors, since most will loose.
--
John Conover, john@email.johncon.com, http://www.johncon.com/