“Fortune’s Formula” is the Kelly Criterion from J.L. Kelly Jr. who was a mathematician at Bell Labs in the 1950s. Essentially the formula gives the optimal size of bets in order to win as much as possible over time while reducing the risk of ruin. The thing for the reader to realize is that the Kelly Criterion has no utility unless the bettor or investor has an advantage. That needs to be repeated: on an even bet, such as tossing a coin the Kelly strategy is to bet nothing, zero, zilch.

Before I get into the review of this excellent and very interesting book I want to relate an experience I had some years ago, sometime in the early 1980s. I thought I had come up with a way to bet on baseball games in Las Vegas with an advantage over the line (that is over the bookie’s vigorish). For a season I studied results compared to the betting line. I was so sure I had a clear advantage that the next problem became how to run up my money efficiently without taking the chance of going broke. In other words, non-mathematician that I am, I was seeking something like Kelly’s Criterion. And what I came up with turned out to be very similar to his formula, although I don’t recall exactly. Unfortunately when I got to Las Vegas it didn’t take me long to realize I had no advantage and therefore didn’t make any bets.

Okay, back to the book. An excellent way to get an idea of the scope of this work is to look at the parts. Part One is titled “Entropy,” Part Two is “Blackjack,” Part Three is “Arbitrage,” Part Four is “St Petersburg Wager,” Part Five is “RICO” (Racketeer-Influenced and Corrupt Organization), Part Six is “Blowing Up,” and Part Seven is “Signal and Noise.” Along the way you will meet gangsters, the Italian and Jewish mafias, a young and very aggressive Rudolph Giuliani, the Hong Kong horseracing scene in which some people made millions (it was the only legal betting allowed by law in Hong Kong) and some keen ideas on how to make money gambling or investing. But what really makes this book so interesting is the light that Poundstone shines on two giants in the science of information, gambling and investing, namely Claude Shannon and Edward O. Thorp.

Shannon is known as the father of information theory and in many respects as the founder of the digital world we live in today. He was also an astute investor as Poundstone reveals. I don’t think it would be an exaggeration to say that Shannon was a genius.

Thorp first became known to the public with his book “Beat the Dealer” (first edition, 1962) which presented a winning strategy for blackjack. I read that book when I was still in my twenties with great enthusiasm but never employed the strategies since my memory is rather ordinary. Instead I played poker, but that, as they say, is another story. What is astonishing about Thorp that I learned here is that his hedge fund, Princeton-Newport Partners was one of the most successful ever. A dollar invested in the fund in 1969 would grow to $14.78 in1988. Yes, wow.

Poundstone explains in detail how all this happened and it is a fascinating story. I’m amazed at how much work he put into this book and all the information he acquired. He is an outstanding and prolific journalist as well as an MIT grad, although I must say that the organization of the book was a bit freestyle. Additionally there are some errors and some unclear passages. Consider this on page 39: Ed Thorp (as a boy) “would buy a pack of Kool-Aid for five cents and sell the mixed beverage to hot WPA workers for one cent a glass. Ed could get six glasses from a pack for a penny profit.”

What is not right here is that you needed to add sugar to the Kool Aid which would be an additional expense.

On page 68, Poundstone writes: “Kelly described his idea this way: A ‘gambler with a private wire’ gets advanced word of the outcome of baseball games or horse races…”

It’s unclear what year this was but regardless of the year you can’t get “advanced word of the outcome” of a baseball game.

One more example: Poundstone writes: “In 1993 Ed Thorp” learned from a computer science person who “had discovered” that pro basketball teams “that had to travel to the city in which a game was played tended to do poorer than a team that didn’t have to travel. A team that had to play a number of games in a row did poorer on average than a team given more rest between games. These variables were not properly weighted in bookies’ odds.” (p. 322)

This is not true even in 1993. The two factors mentioned are just exactly the sorts of factors that are built into the bookies’ betting line, as any serious sports bettor knows.

Part of the pleasure in reading this book is in the way that Poundstone exposes stupidity in what would seem to be high places. Here’s a quote from Mark Rubenstein who is a professor of finance at UC Berkeley. He’s talking about the Black Monday stock market crash of October 19, 1987:

“So improbable is such an event that it would not be anticipated to occur even if the stock market were to last for 20 billion years, the upper end of the currently estimated duration of the universe. Indeed, such an event should not occur even if the stock market were to enjoy a rebirth for 20 billion years in each of 20 billion big bangs.”

Gee, I hope he was just funning us.

(BTW, my baseball betting delusion came about because I used the line in the Los Angeles Herald Examiner which was a stale line that didn’t account for recency. My approach was to weight recent results more heavily that older results. When I got to Vegas and saw the Vegas line it was clear that their betting lines did indeed consider recency.)

--Dennis Littrell, author of “The World Is Not as We Think It Is”

This book is a concise look at the evolution of formal investment theory, with continual contextual references to its ties to gambling and to organized crime. It also is a hilarious and insightful history of gambling from the Bernoulli's in the 1700s through the hedge fund traders of the late 1990's.

The author devotes over 50 pages to notes and the index. This was appreciated since I wanted to look up more about so many of the anecdotes he included.

Mr. Poundstone poignantly describes the downfall of high-flying firms such as LTCM, where the investment wizards went from the darlings of Wall Street to the dredges of the investment community in large part because they were so clever; and they started to believe they were infallible.

One LTCM road-show presentation was held at the insurance company Conseco in Indianapolis. Andrew Chow, a Conseco derivatives trader, interrupted Scholes. "There aren't that many opportunities," Chow objected. "You can't make that kind of money in Treasury markets."

Scholes snapped: "You're the reason - because of fools like you we can." (Page 281)

Warren Buffett marveled at how "ten or 15 guys with an average IQ of maybe 170" could get themselves "into a position where they can lose all their money." That was much the sentiment of Daniel Bernoulli, way back in 1738, when he wrote: "A man who risks his entire fortune acts like a simpleton, however great may be the possible gain." (Page 291)

He also points out the real world flaws in some theoretically appealing scams. The St. Petersburg Wager seems mathematically correct; yet it overlooks a vitally important constraint (pages 182-184). Another is the unfounded weight we unconsciously give to historical returns, as evidenced by his retelling of another Warren Buffett story:

In a 1984 speech, Buffett asked his listeners to imagine that all 215 million Americans pair off and bet a dollar on the outcome of a coin toss. The one who calls the toss incorrectly is eliminated and pays his dollar to the one who was correct.

The next day, the winners pair off and play the same game with each other, each now betting $2. Losers are eliminated and that day's winners end up with $4. The game continues with a new toss at doubled stakes each day. After twenty tosses, 215 people will be left in the game. Each will have over a million dollars.

According to Buffett, some of these people will write books on their methods: "How I Turned a Dollar into a Million in Twenty Days Working Thirty Seconds a Morning." Some will badger ivory-tower economists who say it can't be done: "If it can't be done, why are there 215 us?" "Then some business school professor will probably be rude enough to bring up the fact that if 215 million orangutans had engaged in a similar exercise, the result would be the same - 215 egotistical orangutans with 20 straight winning flips." (Page 314)

The author follows the lives of a few major contributors to investment theory, information theory, and betting theory: Claude Shannon, who invented Information Theory and paved the way for the digital computer age; John Kelly, who developed the formula for gains with no possibility of ruin; and Edward Thorpe, who built upon these findings and beat the roulette wheels, the blackjack tables and the investment fund managers.

It's a fast read - only 329 pages before the notes and index. I highly recommend it!

It's hard to describe what this book is. Is it a primer on betting strategies? A look at practical math? A history of mathematically inclined gamblers? A "mob" story? A manual for cash management in investing?

The book has facets of each, though in the end, the main takeaway is the superiority of the Kelly system for managing bankrolls whether gambling or investing.

For the most part, it is an interesting read though there are sections that bog down. I'd recommend the book as an interesting historical look at some people who tried to beat the house - in gambling or investing - and as a primer on the Kelly method but I wouldn't suggest that anyone head to Vegas or Wall St. with their kid's college savings based on this book.

Someone recommended this book to me as an investment book. At the time I was not sure how gambling and quantitative approach to investment are related. But this book, through its illustration of Kelly's criteria provides a new way to think about investment strategy. I learned all the moot theories in school - Mean portfolio optimization, diversification, efficient market theory, etc. But thinking of information theory, Kelly's criteria and ever present arbitrage can give one quite an edge.

The book interweaves mathematics, history and stories quite well and is a very good read. Imagine an investment book that reads almost like a fiction novel :)

The material is very well researched and it contains history of gambling, and investment and how information theory evolved. The book also gives a view into how a powerful school of thought can eclipse other schools of thought. in this case, Samuelson, et all from MIT refute geometric returns from Kelly's criteria even though working proof is present and the alpha factor in returns is not a myth.

I am glad the person recommended this book to me.

I expected this book to be technical and focus of the Kelly Criterion only. Instead, I found myself exposed to a fascinating and entertaining, historical account of the lives of several mathematicians, academics and professional gamblers. The stories of these men, during from the 1960s to the early 2000s, demonstrate the inspiring intellect and application of knowledge to the challenge of making money.

If true, the book merits five stars. If not true, then the book merits hardly three stars for not being circumspect. If the latter, then the scholarship is quite poor. William Poundstone, author of excellent books on game theory, did not engage in any lateral thinking in this book. I'm skeptical of the purported existence of a "formula" that was used to play the stock market so successfully by these guys. First of all, I submit the possibility that there was no formula and that these guys were engaged in inside trading. If so, then what a clever way of avoiding scrutiny by the Securities Exchange Commission other than explaining your fortune by pointing to some formula. Like a magician employing misdirection, could it be that there was no formula, only inside trading? And if the SEC bought that story, then the inside traders could escape Securities Exchange charges and violations. And this would be the genius of Thorpe and others, not some formula. Like the Rothschilds who exploited their monopoly on carrier pigeons in pre-telecommunications England said Napoleon defeated the British at Waterloo so they could buy British bonds pennys on the dollar, or Joe Kennedy who under Roosevelt regulated securities while fleecing the stock market (an inside job) or Bill Gates who took the somebody else's operating system "BASIC" and sold it to IBM with a contract provision giving him exclusive rights to sell it to the personal user (the innovator of "BASIC" not even privy that this was going on) or Rockefeller buying off railroads to push other oil companies out of the market and avoiding taxes by putting his money in trusts, or the guys who opened King Tut's tomb and looted it and resealed it and then "rediscovered" it so the Egyptian government was robbed of much of the gold in that tomb, perhaps the "Forumla" herein is another example of what Honore' Balsac said, "Behind every great fortune is a crime."

Great read and rings true. Claude Shannon supervised my bachelor's thesis at MIT, the description of Shannon in this book is spot on. With every passing day it becomes clear Shannon was arguably one of the greatest scientists of the 20th century, in the league with Alan Turing, Albert Einstein, Richard Feynman, John von Neumann, and John Nash: Shannon master's thesis is the foundation of all digital circuit logic design which I was taught and millions practice around the globe, while information theory is the basic theory underpinning modern optical, copper wire and wireless networks.. One of the amazing things about information theory was that Shannon showed an intrinsic rate was present in communications, and called this channel capacity: if you exceeded it, errors grew, while if you stayed below it, arbitrarily great accuracy could be achieved: no one had ever claimed that before Shannon. I did listen to a lecture by Shannon at MIT on financial portfolio investments: the hall was packed to overflowing, every word was being scrutinized. My long time colleague at Bell Labs worked directly with John Kelly, and everything about Kelly rings true in this book. One wonders what new environment will nurture the creativity that Bell Labs fostered in the middle of the twentieth century. It is no wonder that Warren Buffet uses Kelly's criterion in validating investment decisions: it cost little, yet it can help prevent egregious error!

"Fortune's formula" is the author's cute name for what mathematicians call the Kelly criterion. Much of the book is entertaining episodic anecdotal history of characters like Shannon, Kelly, Thorp, Milken, Boesky and Long Term Capital Management. The formula-free discussion of mathematical aspects of the Kelly criterion is rather good (to my taste as a professional mathematician). Entertaining account of dispute between the proponents of Kelly (math types) and economists led by Samuelson who viewed it as too risky even in the long run. Memorable slogan: 100% Kelly strategy marks the boundary between aggressive and insane investing.

To lecture briefly ..... in a hypothetical gambling or investment situation where you have a range of choices to bet on/invest in, and where you know the correct probability and profit/loss from each possible outcome, the Kelly criterion tells you how to split your investment between the different choices. The point of the formula is to take into account the fact that (when investing all your money) a 20% gain one year followed by a 20% loss next year works out as a 4% loss, not zero. Its use in splitting beween risky and safe investments is uncontroversial. People get emotional about the "efficient market hypothesis" that you cannot assess probabilities for future stock prices more accurately than the consensus probabilities reflected in current prices; but this is an empirical question, like asking "can you beat Tiger Woods at golf", and of course has the same answer for most people. Poundstone conveys such concepts pretty well.

Other reviewers have remarked on how entertaining this book is; those who have read some of Poundstone's other works will find this no surprise. There are some wonderful anecdotes and insights here, with hard-ish science mixed in nice pen-portraits of the main protagonists.

However, having an interest in sports betting and investment, I also found the book very helpful in explaining the benefits and potential pitfalls of the Kelly approach (as Poundstone mentions, there is still antipathy towards the approach among some gambling experts who really should know better). In particular, he takes pains to explain why Kelly succeeds over both level staking and Martingale systems, and how volatility can be controlled through reduction in Kelly proportions and also diversification. I have benefited personally for these and other insights in the book, which I can thoroughly recommend.

Excellent book worth taking the time to read and understand.

The book covers subject of scientific betting system developed by great minds like Claude Shannon and Ed Thorp. They used the system to beat casinos to start with and then used same principles to earn handsome returns in stock markets. The author has developed a dry subject into an interesting read with topics covering stories of mafias, casinos and activism of the likes of Rudy Giuliani, LTCM fiasco etc. Every story eventually leads to betting system and betting syndicates. In the process the author has explained the Kelly criterion in great details with ample examples of its practical use by successful investors and portfolio managers. We are also introduced to the genius of Claude Shannon, the father of Information Theory and Digital Revolution.The book is a must read for every serious investor. The book is highly recommended by no less than Charlie Munger.

This is a really interested book. I thought is started out a little slow and was hard to get into, but it picks up. It's super interesting how mathematical everything is. The book is good if you are into casinos and gambling, stock markets and wall street, or simply trying to money, as it blurs the line between wagering and investing which almost comes down to being the same thing. It is a good read and provides a fascinating look into how a couple guys developed a formula for making money.

Entertaining from the start till the end. Another great book from Poundstone shedding lights on fabulous characters of the 20th in various fields ranging from the fringe of the society to the scientific world.

As usual the reader will gain great insight on the many topics covered.