From: John Conover <firstname.lastname@example.org>
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, email@example.com, http://www.johncon.com/