It’s a commonplace in science that we care about the last word, not the first. Once a puzzle has been recognized, all kinds of solutions are proposed: conjectures, speculations, proofs clumsy or flawed. Many are useful. Some come tantalizingly close. Then someone finally poses the problem with sufficient clarity, and somebody else solves with sufficient depth, that all the rambunctious prelude is forgotten. The right answer, the preferred solution, enters the texts and is adopted into practice.

A lively glimpse of this process going forward in economics can be found in Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street. Its author, William Poundstone, is the Damon Runyon of science writers. *Fortune’s Formula* is his tenth book.

His other works include interpretive biographies of John von Neumann and Carl Sagan; an extended meditation on mathematician John Conway and his game of Life (“The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge”); an exploration of corporate R&D practices called How Would You Move Mount Fuji? Microsoft’s Cult of the Puzzle — *How the World’s Smartest Companies Select the Most Creative Thinkers*; *The Big Book of Big Secrets: The Uncensored Truth about All Sorts of Stuff that You Are Never Supposed to Know*; and *A to Izzard*, a companion to the works of novelist Harry Stephen Keeler (here the link is definitely worth following!)

In the case of *Fortune’s Formula*, Poundstone’s heroes are three men who shared a vivid interest in making money by beating financial markets, though each expressed it in a slightly different way. They are Claude Shannon, the engineer who founded modern information theory at Bell Laboratories; Edward Thorp, a mathematician who collaborated with Shannon when they overlapped for a time at the Massachusetts Institute of Technology, before setting out on a long career as an investor; and John Kelly Jr., a Bell Labs physicist who came up with a controversial formula for betting (or investing, if you prefer) that since has become known as the Kelly criterion.

The book is populated with colorful incidental characters, as well: horse-race tout sheet pioneers John Payne and Moe Annenberg; mobsters Longy Zwillman and Ben “Bugsy” Siegel; G-man J. Edgar Hoover and US attorney Rudolph Giuliani; economists Paul Samuelson and Robert Merton; science fiction authors L. Ron Hubbard and Arthur C. Clarke; conglomerateurs Emmanuel Kimmell and Steve Ross (they built Time-Warner); filmmakers Robert Evans and Mario Puzo; and hedge fund operators Ivan Boesky and John Meriweather (of Long Term Capital Management). All mix and mingle in his pages. But it is the lives of Shannon, Kelly and Thorp that provide Poundstone with his narrative thread. His book might not point to a neat satisfying conclusion (unless it is that the world is enduringly messy), but it sure is fun to read.

Of the three central figures, Shannon is the best known. (He died at 84 in 2001.) Poundstone counts him among the two or three basic inventors of the computer, for his suggestion that Boolean algebra and binary code — simple 0’s and 1’s — would be sufficient to convey in switches and store in a computer words, sounds, pictures, indeed any sort of information. But his greater fame rested on a paper he published in 1948, A Mathematical Theory of Communication.

Ostensibly addressing the relatively simple engineering problem of sending a message quickly, efficiently and cheaply via telephone or television, Shannon’s paper offered a powerful analogy between information and energy — a way to understand signal and noise and manipulate the chance of error with a precision previously undreamt of. Shannon’s discovery made him famous overnight, and brought him to MIT. But within a few years he had lapsed into relative silence, in favor of his hobby, investing in the stock market.

Shannon met Thorp in 1960. The junior faculty member wanted to publish a paper he called “A Winning Strategy for Blackjack.” (The trick was to count the cards and play according to whatever remained undealt.) Would Shannon send it for him to the *Proceedings of the National Academy of Sciences*? Certainly, but only if he changed to title to something more sedate: “A Favorable Strategy for Twenty-One.”

Before long, Thorp and Shannon were working together evenings in Shannon’s basement on a gadget designed to predict the likely fall of the ball on a spinning roulette wheel, assuming that the wheel had some slight imperfection that could be quickly detected. (Roulette has long held a fascination for the statistically-oriented. In Grammatical Man: Information, Entropy, Language and Life, Jeremy Campbell relates how a youthful John Maynard Keynes and three friends once dashed for the night ferry to Ostend after being told that roulette was played there without a zero.)

Thorpe tried his hand at counting cards for a time. It was a another decade before a band of California pranksters actually built his roulette device and tried to use it, an episode described by Thomas Bass in The Eudaemonic Pie. By then, however, Thorp had discovered the stock market. He gave up casinos and began trading warrants, an old-fashioned form of stock option. In 1969, he started a hedge fund with a stockbroker friend that in due course they would name Princeton-Newport Partners. At the height of insider trading scandals in 1988, with several of its executives facing RICO indictments, Thorp (who was not among them) liquidated the fund.

Kelly is the most enigmatic of the three. Born in 1923 in Corsicana, Texas, he was on his way to becoming a petroleum geologist when Bell Labs hired him in 1953 as a material scientist. An avid gun enthusiast and football fan, he was a colorful figure in the New Jersey suburbs. He specialized in television data compression, with a sideline in voice synthesis — it was he who programmed the computer to sing “Daisy Bell” (“A Bicycle Built for Two”) that found its way into “2001 — A Space Odyssey” after he showed it to screenwriter Arthur Clarke. But his fame today rests on his invention of a betting system — a system inspired, he told an interviewer, by the revelation that the hit 1950s quiz show “The $64,000 Question” had been fixed.

Where Shannon and Thorp had concerned themselves with ways to elicit information from markets, Kelly’s starting point was to suppose he already had it. He imagined he had a source of inside information — a private wire to a race track, or advance warning of a fix. Such tips might not always be right, but they would be reliable enough to give the better an edge. What, then, should the savvy bettor do? Not bet the whole bankroll, that’s for sure; the first time the tip was wrong, he’d lose everything. Conversely, a cautious bettor would make far less than he might. What was the optimum strategy for a gambler with inside information? Kelly concluded found that the math Shannon had used to manage noisy channels of communication, systematically correcting for the measure of ambiguity that he called *equivocation*, applied with equal force to bettors dealing with uncertainty.

Explains Poundstone: “Kelly described a simple way for a gambler with inside tips to bet. The strategy is to bet your entire bankroll on each race, apportioning it among horses according to your informed estimate of each horse’s chances of winning. With this system, you bet on every horse running. One horse *has* to win. You can never end up completely broke. Strangely enough, this is also the *fastest* way to increase your bankroll… When you believe that War Admiral has a 24 percent chance of winning, you should bet 24 percent of your capital on War Admiral. …In the long run, [this] ‘bet your beliefs’ will earn you the maximum possible compound rate — provided that your assessment of the odds is more accurate than the public’s.” The story of the Kelly system, writes Poundstone, “is a story of secrets….”

The nemesis of this Bell Labs reasoning was developing at the University of Chicago in the mid-1960s, in the form of the “efficient markets hypothesis.” This was the conviction that the prices of assets traded in financial markets already contain most if not all the relevant information known to market participants, in which case stock prices would follow a “random walk.” The implication of this subtle reasoning is that the market is so good at collecting information and setting prices that there can be no meaningful “inside information.” Nobody beats the market over time except through sheer good luck.

All these matters suddenly converged in the late 1960s on the question of the pricing of options. Options were nothing new. The right to sell an asset at a given price on a certain date (a put) or buy it (a call) had been actively traded in Europe since the seventeenth century. What was new was the precision with which the value of options could be described. Ed Thorp devised a formula to identify options that were severely overpriced or underpriced, and therefore surefire bargains. In Cambridge, Massachusetts, so did Fischer Black and Myron Scholes. There was a crucial difference. Black and Scholes had a term in their formula for the interest that could be earned on the sale of an option.

In a remarkable series of events that have been related by, among others, Peter Bernstein in *Capital Ideas*, Perry Mehrling in *Fischer Black and the Revolutionary Idea of Finance* and Donald McKenzie in *An Engine, Not a Camera* (more on the latter two books next week), Black and Scholes published their options pricing formula in 1973; Robert Merton generalized their results; and Thorpe was left with a near-miss. Merton and Scholes shared a Nobel Prize the year after Black died. Thorp is philosophical. “I never thought about credit, actually,” he explained to Poundstone, “and the reason is that I came from outside the economics and finance profession. The great importance that was attached to this problem wasn’t part of my thinking. What I saw was a way to make a lot of money.”

All this is related to good effect in “Fortune’s Formula.” Thorp went on to make a lot more money using techniques of statistical arbitrage. So did Shannon, who was said to have had a rate of return of about 28 percent on his portfolio over thirty years, compared to 27 percent for Warren Buffet. Shannon’s success owed not to any fancy statistical technique, but rather to simple buy-and-hold fundamental investing. Kelly, who wasn’t interested in making money, died of a brain hemorrhage on a Manhattan sidewalk in 1965, at the age of 41. But interestingly enough it is the “Kelly criterion” that has lingered on.

Poundstone describes the small group of Kelly economists and money managers who have kept the flame alive: their battles with Paul Samuelson over the logic of their math (“a complete swindle,” wrote the great economist at one point); their conviction that Kelly-style caution would have prevented John Meriweather’s Long Term Capital Management from imploding, with potentially ruinous effect on global financial markets; their sense that extremely improbable possibilities such as depressions, plagues and wars should routinely be taken into account.. “It’s a story with everything but an ending,” Stanford information theorist Thomas Cover told Poundstone, expressing his conviction that the unorthodox view of the salience of extremely low-probability events may eventually win out.

And so it might. Stranger things have happened in science. William Poundstone has given a wonderful account of the state of play.