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Roulette, Mispriced Bets and Investing

Joseph Jagger, born in September 1830 in a village near Bradford, Britain, was an engineer in a cotton factory in Yorkshire.

With years of practical experience in the cotton manufacturing industry, Jagger developed an intuitive feel about what machines could do. He figured that even the most sophisticated instruments are far from mechanical perfection. Every machine has flaws. And every flaw brings with it an opportunity to exploit it.

The Englishman often wondered if it was possible to convert his expertise into more cash, not by scamming his employer at the cotton factory but by discovering the possible flaws in the gambling machines at Monte Carlo? Especially the roulette wheels.

In 1873, Joseph Jagger became the first man to break the bank at Monte Carlo.

The Beaux-Arts Casino at Monte Carlo, Monaco was inaugurated in 1863. In Beaux-Arts casino, at the start of the day, every table was funded with a cash reserve of 100,000 francs – known as ‘the bank’. François Blanc, the original owner of the casino, devised a rule for the Casino. If any gambler won more than the cash allocated for the table, the play was temporarily suspended and a black cloth was laid over the table in question. This ceremony was called breaking the bank. After an interval, while extra funds were brought out from the casino’s vaults, the table re-opened and play continued.

To understand Jagger’s scheme, we need to wrap our heads around the dynamics of roulette wheel betting.

Ready for a crash course?

According to a legend, roulette was invented by 17th-century mathematician Blaise Pascal as he was tinkering with the idea for the perpetual-motion machine. A roulette is basically a large bowl with partitions (called frets) that are shaped like thin slices of pie. These pie-shaped compartments are numbered 0 through 36, i.e., total 37 numbers.

At the start of the play, the wheel is spun and a white marble is thrown into the roulette. The marble bounces along the rim of the bowl and eventually comes to rest in one of the compartments. The bettor’s job is to guess the compartment the marble will land.

In Monte Carlo, if you bet $1 on a number and the marble lands on that number, the house (Casino) pays you $35 (plus your initial dollar).

So, your odds of winning is 1 out of 37. And your chances of losing? 36 out of 37.

It means that for every $1 you bet, the Casino stands to win [(36/37) x ($1) – (1/37) x ($35)]. That amounts to 1/37 of a dollar, i.e., about 2.7 cents. In other words, the Casino has a positive expected value for each bet.

Although this expected value per bet is minuscule, when you multiply it by thousands of such bet happening every day across multiple roulette wheels, the Casino comes out as the winner.

But all that mathematics is based on the assumption that the roulette wheel is perfectly balanced and unbiased and the probability of each number is equal, i.e., 1/37.

Having worked with enough machines, Jagger was willing to bet that some, if not all, roulette wheels might have a bias toward certain numbers. So he gathered all his savings and arrived at Monte Carlo.

His plan was to first identify those unfair roulette wheels. So, like Daniel Ocean from the movie Ocean’s Eleven, he assembled a team of six clerks. Jagger’s Six, if you will. One clerk for each of the casino’s six roulette wheel.

Every day Jagger’s men closely observed the wheels, noting down all the winning numbers during the entire day. Every night, they handed this data to Jagger. After analysing six days of data, Jagger had not detected any bias in five of the wheels, but on the sixth wheel nine numbers came up noticeably more often than the others.

Jagger found what he was looking for – a mechanical flaw which skewed the odds in his favour.

On the seventh day, Jagger walked into Beaux-Arts Casino and started betting heavily on the nine favoured numbers: 7, 8, 9, 17, 18, 19, 22, 28, and 29. By the end of the day, Jagger had won enough to attract the attention of other gamblers in the casino.

Soon, Jagger’s roulette table was swarmed by other bettors. It was a bad news for the casino.

For next four days, Jagger continued winning and casino inspectors kept scratching their heads trying to decipher Jagger’s betting system. Casino guys even suspected Jagger of cheating but there was no way to prove it.

However, on the fifth day, Jagger’s winning streak stopped abruptly. He began to lose. His losing, like his winning, was not something one could spot immediately. He would win some and lose some, however, he lost more often than he won instead of the other way around.

By the time Jagger realised that his trick wasn’t working anymore, he had lost half his fortune that he had amassed during the first four days of winning. Now, it was Jagger’s turn to scratch his head.

After much introspection, it suddenly occurred to him that he had been noticing a tiny dent on the roulette wheel. This mark was missing on the fifth day. Next day, Jagger inspected the other five roulette wheels and found that dent in one of them.

The casino managers had correctly guessed that Jagger’s lucky run was somehow connected to the wheel he was playing. So they cleverly switched the wheels.

Jagger relocated to the table which had the dented wheel and promptly started winning again. A cat and mouse game was about to ensue but casino managers soon found an innovative way to thwart Jagger permanently. They would move the frets each night turning them along the wheel so that each day the wheel’s imbalance would favour different numbers unknown to Jagger.

Jagger folded and left Monte Carlo with £120,000 in hand. That is roughly equivalent to $12 million in today’s money. Back home in Yorkshire, he quit his cotton mill job, invested the casino winnings in real estate and never gambled in his life again.

Jagger’s story was first chronicled in Victor Bethell’s book Monte Carlo Anecdotes and Systems of Play which was published in 1901. Some people later questioned the authenticity of Jagger’s story suspecting that Bethell might have created it for his book. However, historian Anne Fletcher, in his book From the Mill to Monte Carlo, (due for release in July 2018) has written a biography of Joseph Jagger which includes persuasive evidence that Jagger did in fact break the bank of Monte Carlo.

Does Joseph Jagger’s story have any lessons for investors? Plenty.

The first lesson is that although Jagger was in a casino, he wasn’t really gambling. He understood the idea of odds very well and he recognised that the biased roulette, because of its flaw, offered a mispriced bet.

Charlie Munger once said –

To us, investing is the equivalent of going out and betting against the pari-mutuel system. We look for a horse with one chance in two of winning, and that pays three to one. In other words, we’re looking for a mispriced gamble. That’s what investing is, and you have to know enough to know whether the gamble is mispriced.

When a horse with one chance in two of winning, offers a payout of two to one, then it’s an efficiently priced gamble. There’s is no edge for the gambler in such bets. If you understand this then it’s not really gambling. Similarly, it’s not investing if one doesn’t know what he is getting into.

The second lesson is about having informational edge. Jagger had an informational edge, i.e., he knew that there was a roulette which was imbalanced.

Legend has it that young Warren Buffett often used to count the train cars as a way to gauge the change in the overall economy.

Investors who follow Philip Fisher’s scuttlebutt strategy are essentially trying to get this informational edge. It reminds me of how a famous Indian value investor used to visit the retail stores and check the manufacturing date of the products on the shelf. During one such visit he stumbled upon a very interesting finding.

There were two undergarment brands that were on the shelves – Hanes and Jockey. Most of the Hanes boxes had old packaging dates while Jockey’s stock was very new. He concluded that Jockey was selling more than Hanes. That’s how he found Page Industries much before the others.

The third lesson is about the analytical edge. Jagger combined his informational edge with an analytical edge, i.e., figuring out those nine numbers that biased roulette wheel favoured. Having the information is not enough. You need to have special insights derived from the information which is public and available to everyone.

Ankur Jain’s recent blog post is a brilliant example of how analytical insight are derived from publicly available information.

As much cool and intellectual it sounds, having an informational and analytical edge in today’s world is extremely hard for small investors like you and me.

So, the final and most important lesson that I draw from Jagger’s story is about knowing when to fold.

Jagger’s intelligence wasn’t only in devising the scheme but also in recognising when the odds ceased to be in his favour. He never gambled again because he knew that casinos had become more efficient.

I have learned that I tilt the roulette wheel of investing in my favour when I …

  • Avoid personal debt
  • Invest for the long-term
  • Avoid companies that have highly leveraged balance sheets
  • Avoid companies that have management with a questionable history
  • Avoid IPOs
  • Avoid derivatives

How about you? Do you know when the odds are in your favour?

Note: I discovered Joseph Jagger’s story in Leonard Mlodinow’s brilliant book The Drunkard’s Walk. Further research on the internet fetched me more details about Jagger which I have added to the narrative above.

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About the Author

Anshul Khare worked for 12+ years as a Software Architect. He is an avid learner and enjoys reading about human behaviour and multidisciplinary thinking. You can connect with Anshul on Twitter.


  1. Mastram says:

    We can say the odds are in favour of a person only if he is born to a billionaire. Everything else is speculation on roulette wheel 🙂

  2. Sabyasachi Sadhu says:

    For us traders present time is a bliss, we don’t give a damn about the future, we “enjoy” as much as possible in present time. Value Investing is a boring subject. We just believe in instant gratification rather delayed gratification. Who has seen the future so live happy right this very moment. Value investing is for academia, trading is for the real people with practical value.

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