Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
William Poundstone, 2005
If you have an edge in a game or in the market, how much money should you bet? William Poundstone's story runs from racetracks and casinos to Wall Street and explains the Kelly criterion, which linked information to the growth of capital. You'll see that this formula can only guide you when you really do have an edge, and why a wrong estimate or an oversized bet changes everything.
Who it is for
For anyone who wants to understand financial risk, tell a real edge from luck, and see why the same calculation can help you win and can also lead to ruin.
Daniel Bernoulli: “A man who risks his entire fortune acts like a simpleton, however great may be the possible gain.”
The seconds on which fortunes were bet
John Payne set up a service that sent horse race results by telegraph. Bookmakers who got the news before anyone else could keep taking bets while the public still didn't know the outcome. Information by itself didn't make a horse run faster, but it changed the odds for those who managed to react to it in time. Later this story became entangled with organized crime and American telephone networks.
Years afterward, the physicist John Kelly described a similar situation in mathematical terms: a gambler gets news of a race over a private wire and knows a little more than everyone else. His question was unexpected. If your knowledge gives you an edge, what share of your fortune should you bet so that you don't miss out on growth and don't lose everything?
William Poundstone connects this problem with Claude Shannon, the creator of information theory, and with the mathematician Ed Thorp, who tested ideas in casinos and then in the financial markets. Their stories show that the Kelly formula helps determine the size of a bet only once an edge has already been found. It doesn't predict the result and doesn't protect you from a wrong calculation.
What matters for you here isn't a recipe for getting rich quick but a way of thinking about risk. We'll go from counting cards to stocks, from an infinite expected payoff to human limits, and then look at why smart people go broke anyway. Let's start with what can count as an edge in the first place.
Kelly turned information into the size of a bet
Payne's telegraph service mattered not because it guessed the outcomes of races but because it delivered them faster. At the racetrack, the gap between the first news and the last changed the price of information. The service became a big business, and control of it passed to people with ties to the underworld. Poundstone opens with this story to show that luck and an edge look alike until you ask what exactly the gambler knew and when he found out.
At Bell Labs, Claude Shannon was looking for a way to measure information. That is how information theory was born. Entropy, a measure of a message's uncertainty, shows how hard it is to guess an outcome in advance; if a signal narrows down the possible options, it lowers uncertainty. The more a signal changes your odds, the more information it carries. Information is like a flashlight in a dark hall: it doesn't create objects, it helps you notice what's already there.
John Kelly applied this idea to the gambler with a private wire. If the gambler can predict the outcome of races more accurately than the odds reflect, his task isn't to bet as much as possible. He has to match the bet to the size of his edge. Later the rule came to be called the Kelly criterion: it ties the share of capital you stake to the chance of winning and the payout. If there is no edge, the calculation says not to bet.
Kelly maximized not a single win but the rate at which money grows over the long run with repeated bets. That's why the formula is especially sensitive to how the odds are estimated. If the edge looks bigger than it is, the model tells you to bet too much. Before doing any math, name the specific signal, check whether it changes the probability of the result, and compare that probability with what's already built into the odds. As long as the source of the edge is unclear, the formula won't turn a guess into knowledge.
The value of a signal depends not only on its accuracy but also on timing. A bookmaker can change the odds, and another gambler can react sooner. Once everyone has taken the news into account, it no longer gives anyone a head start. Before you bet, pin down which event the signal predicts, how much it changes the probability, and whether you have time to use it before the price changes.
This distinction matters for investing too: the market can price in news before you have time to react. If the net payoff equals the amount bet and the probability of winning is estimated at 60 percent, the full Kelly criterion suggests betting 20 percent of your capital. This is a hypothetical example: a mistake in estimating the probability also distorts the calculated share.
About the author
William Poundstone is an American author of popular science books who studied physics at the Massachusetts Institute of Technology. In his work, mathematical ideas step out of the textbooks and shape the decisions people make.
All books by this author: William Poundstone
Terms from the book
- Samuelson
- Blackjack
- Expected value
- Kelly
- Thorp
- Bell Labs
- Entropy
- Kimmel
- Bernoulli
- St. Petersburg paradox
- Utility
- Warrant
- Arbitrage
- Long-Term Capital Management
- Meriwether
- Merton
- Scholes
- Liquidity
- Leverage
- Correlation
- Woods
- Buffett
- Payne: John Payne, the man who organized a telegraph service that sent horse race results to bookmakers.
- Shannon: Claude Shannon, an American mathematician and engineer. He laid the foundations of information theory and studied gambling and investing.
- Information theory: A branch of mathematics about how to measure and transmit information, including how much a message reduces uncertainty.
- Kelly criterion: A rule for calculating what share of capital to stake on a bet with a positive edge. In an ideal model it maximizes the long-term growth rate, but the result depends on how accurately the odds are estimated.
- Hand: Eddie Hand, a gambler and business partner of Manny Kimmel who took part in the trip to Nevada with Thorp.
- Fama: Eugene Fama, an American economist known for his research on the efficiency of financial markets.
- Princeton-Newport: The investment partnership of Ed Thorp and Jay Regan, which used mathematical analysis and arbitrage strategies.
- RICO Act: A US law passed to prosecute organized crime and later also applied to cases involving financial schemes.
- Benter: Bill Benter, an American mathematician and gambler who built a computer model for betting on horse races in Hong Kong.
All terms
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