In this book the author John Allen Paulos describes, see full example below, how a random stock pick performs worse than following the newsletter, but I don't understand why. I am still convinced the odds should be 10% for both parties. So, assuming this example is correct. What am I missing? Could someone expand upon this?
A contrived but interesting illustration of a self-fulfilling belief involves a tiny investment club with only two investors and ten possible stocks to choose from each week. Let's assume that each week chance smiles at random on one of the ten stocks the investment club is considering and it rises precipitously, while the week's other nine stocks oscillate within a fairly narrow band. George, who believes (correctly in this case) that the movements of stock prices are largely random, selects one of the ten stocks by rolling a die (say an icosehedron—a twenty-sided solid—with two sides for each number). Martha, let's assume, fervently believes in some wacky theory, Q analysis. Her choices are therefore dictated by a weekly Q analysis newsletter that selects one stock of the ten as most likely to break out. Although George and Martha are equally likely to pick the lucky stock each week, the newsletter-selected stock will result in big investor gains more frequently than will any other stock. The reason is simple but easy to miss. Two conditions must be met for a stock to result in big gains for an investor: It must be smiled upon by chance that week and it must be chosen by one of the two investors. Since Martha always picks the newsletter-selected stock, the second condition in her case is always met, so whenever chance happens to favor it, it results in big gains for her. This is not the case with the other stocks. Nine-tenths of the time, chance will smile on one of the stocks that is not newsletter-selected, but chances are George will not have picked that particular one, and so it will seldom result in big gains for him. One must be careful in interpreting this, however. George and Martha have equal chances of pulling down big gains (10 percent), and each stock of the ten has an equal chance of being smiled upon by chance (10 percent), but the newsletter-selected stock will achieve big gains much more often than the randomly selected ones.