# Chance News 7

Sept 26 2005 to Oct 15 2005

## quotation

While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won.

Joe Doob
Statistical Science

## Forsooth

Peter Winkler suggested our first forsooth.

Texas beats Ohio State in their opening game

of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have previously played in the championship game (at the end of each season) 5 have suffered an earlier defeat. "Thus," they conclude, "Ohio State can still make it to the championship game, but their chances are now less

than 50%."

### Discussion

What is wrong with this?

Here are two forsooths from a recent issue of RSS NEWS

'Big ticket quiz' at the start of Wimbledon:

Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledone tournament?

Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?

20 June 2005

Waiting time for foot surgery down by 500%

Evening News (Edinburgh)
5 July 2005

## Fortune's Formula

Fortune's Formula: Wanna Bet?
New York Times Book Section, September 25, 2005
David Pogue

This must be the kind of review that every Science writer dreams of. Pogue ends his review with:

"Fortune's Formula" may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.

The author William Poundstone is a science writer who has written a number of very successful science books. His book "Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb" was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:

This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read.

Pounstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work here.

Fortune's Formula is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics.

In the spring of 1955 while a graduate student at UCLA Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball and in these seconds, he could estimate what part of the wheel the ball would stop.

Thorp did not pursue this and in 1959 became an instructor in math at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on The Proceedings of the National Academy of Sciences. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out.

Of course Thorpe is best know for showing that blackjack is a favorable game and giving a method to explote this fact. Shannon is best know for his work in information theorly. Kelly is known his method for gambling in a favorable game. This plays a centrl role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09.

Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:

Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a$800 return on your original $10,000 for 8 percent. Peter Doyle suggested that a better investmant strategy in this case is: Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20 percent, you should invest 20 percent of your funds in the risky investment and 80 percent in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. Peter is using a money management system due to J. L. Kelly (A new interpretation of information rate, Bell System Technical Journal, 35 (1956). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. We start with an initial capital, which we choose for convenience to be$1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where $f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)).$