C&B Notes

Redefining the Odds

This remarkable story about Bill Benter, who built an algorithm that cracked the code of horse racing and generated billions in winnings, reminded us of Charlie Munger’s analogy of the stock market as a pari-mutuel betting system.  Both John Kelly, Jr. and Ed Thorp, who have influenced our thinking around position sizing, make interesting appearances.

Veteran gamblers know you can’t beat the horses.  There are too many variables and too many possible outcomes.  Front-runners break a leg.  Jockeys fall.  Champion thoroughbreds decide, for no apparent reason, that they’re simply not in the mood.  The American sportswriter Roger Kahn once called the sport “animated roulette.”  Play for long enough, and failure isn’t just likely but inevitable — so the wisdom goes.  “If you bet on horses, you will lose,” says Warwick Bartlett, who runs Global Betting & Gaming Consultants and has spent years studying the industry.  What if that wasn’t true?  What if there was one person who masterminded a system that guaranteed a profit? One person who’d made almost a billion dollars, and who’d never told his story — until now?

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Benter had been enraptured by Beat the Dealer, a 1962 book by math professor Edward Thorp that describes how to overcome the house’s advantage in blackjack.  Thorp is credited with inventing the system known as card counting:  Keep track of the number of high cards dealt, then bet big when it’s likely that high cards are about to fall.  It takes concentration, and lots of hands, to turn a tiny advantage into a profit, but it works.

Thorp’s book was a beacon for shy young men with a gift for mathematics and a yearning for a more interesting life.  When Benter got to Las Vegas, he worked at a 7-Eleven for $3 an hour and took his wages to budget casinos.  The Western — with its dollar cocktails and shabby patrons getting drunk at 10 a.m. — and the faded El Cortez were his turf.  He didn’t mind the scruff.  It thrilled him to see scientific principles play out in real life, and he liked the hedonistic city’s eccentric characters.  It was the era of peak disco, with Donna Summer and Chic’s Le Freak all over the radio.  On a good day, Benter might win only about $40, but he’d found his métier — and some new friends.  Fellow Thorp acolytes were easy to spot on casino floors, tending to be conspicuously focused and sober. Like them, Benter was a complete nerd.  He had a small beard, wore tweedy jackets, and talked a lot about probability theory.

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Between races, Benter struggled to make his algorithms stay ahead of a statistical phenomenon called gambler’s ruin.  It holds that if a player with limited funds keeps betting against an opponent with unlimited funds (that is, a casino, or the betting population of Hong Kong), he will eventually go broke, even if the game is fair.  All lucky streaks come to an end, and losing runs are fatal.  One approach—familiar to Benter from his blackjack days—was to adapt the work of a gunslinging Texas physicist named John Kelly Jr., who’d studied the problem in the 1950s.  Kelly imagined a scenario in which a horse-racing gambler has an edge: a “private wire” of fairly reliable tips.  How should he bet?  Wager too little, and the advantage is squandered.  Too much, and ruin beckons.  (Remember, the tips are good but not perfect.)  Kelly’s solution was to wager an amount in line with the gambler’s confidence in the tip.

Benter was struck by the similarities between Kelly’s hypothetical tip wire and his own prediction-generating software.  They amounted to the same thing: a private system of odds that was slightly more accurate than the public odds.  To simplify, imagine that the gambling public can bet on a given horse at a payout of 4 to 1.  Benter’s model might show that the horse is more likely to win than those odds suggest — say, a chance of one in three.  That means Benter can put less at risk and get the same return; a seemingly small edge can turn into a big profit.  And the impact of bad luck can be diminished by betting thousands and thousands of times.  Kelly’s equations, applied to the scale of betting made possible by computer modeling, seemed to guarantee success.

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