Probability calculation in stock picking example from the book 'A mathmatician plays the stock market' 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.

 A: The key is the distinction between "a stock has big gains" and "a stock results in big investor gains". In the second case, the stock must both be smiled upon by chance, and selected by one of the investors.
For example, the probability that a particular stock is chosen by at least one of the two investors is 19%, and the probability that it realizes big gains that week is 10%, so the probability that the stock results in big investor gains is 1.9% (over one year, you would expect this stock to result in big investor gains once).
The probability that the newsletter-recommended stock is chosen by at least one of the two investors is 100% (since Martha always chooses it) and the probability that it realizes big gains that week is still 10%, so the probability that the newsletter stock results in big investor gains is 10% (over one year, you would expect the newsletter stock to result in big investor gains five times).
At the end of the year, Martha and George could look back at their results, and would (in expectation) see that the newsletter stock resulted in big gains for at least one of them around 5 times more often than a randomly selected stock did. Not because the newsletter had any predictive power, but just because the newsletter stock was more likely to be in their portfolio.
