Thorp is credited with developing the card counting system, which involves keeping track of high cards dealt and betting big when high cards are likely to come up next. This method requires concentration and extensive practice to turn a small advantage into a profit, but it can be effective.
Book that motivated Bill
Thorp's book inspired shy young men with mathematical talents to seek out more interesting lives. When Benter arrived in Las Vegas, he took a low-wage job at 7-Eleven and used his earnings to play at budget casinos like the Western and El Cortez. Despite the dingy environments, Benter was thrilled to see scientific principles applied in real-world gambling. He enjoyed the eclectic characters of the hedonistic city during the peak of the disco era. Though Benter might only win around $40 on a good day, he had found his calling and made like-minded friends. These fellow Thorp devotees were easy to spot in casinos, tending to be intensely focused and sober. Benter himself fit this mould, with a small beard, tweed jackets, and a penchant for discussing probability theory.
From Zero to Hero
In 1980, he had recently applied for a night cleaning job at McDonald’s when his friends introduced him to Alan Woods, a pivotal figure in his life. Woods, in his mid-30s at the time, had a distinguished grey hairdo and piercing blue eyes. Formerly an insurance actuary with a conventional family life, Woods had forsaken it all to become a globetrotting gambler.
Benter was captivated by Woods' audacious tales, like the one where he snuck through airport security in Manila with $10,000 hidden in his underwear. What truly drew Benter in was Woods' disciplined approach to card counting. The team operated with a shared bankroll and winnings were divided evenly, reducing individual risk and fostering a sense of camaraderie. Impressed, Benter joined forces with them.
Soon, he found himself playing blackjack in the elegant environs of Monte Carlo, feeling akin to James Bond as waiters in formal attire attended to him. His earnings soared to approximately $80,000 annually, leading him to forsake any thoughts of returning to college. When queried about his studies, his mother informed acquaintances that he was currently travelling. Benter and his colleagues settled in a suburban Vegas house, living a lifestyle reminiscent of geeky college fraternity brothers.
Under Woods' strict rule against drinking on duty, they'd wait until after their shifts to share beers and swap stories of encounters with vigilant casino security, who were perpetually on the lookout for card counters. Burly pit bosses patrolled the premises, ready to eject suspicious players or subject them to interrogation in dingy backrooms. There were rumours of harsh treatment, with some counters allegedly being assaulted or drugged. Benter viewed such treatment as unjust; he wasn’t cheating, just playing intelligently.
Bad Reputation
After a few years, Benter was quietly playing at the Maxim when a heavy hand landed on his shoulder. "Come with me," said a large man in a suit. In a back room, Benter was pushed into a chair and asked for identification. He refused. The guard left, and an even more intimidating man entered: "Show me your ID!" Benter reluctantly took out his wallet.
Sometime afterwards—probably around 1984—Benter, Woods, and some of their associates were added to the Griffin Book, a blacklist circulated to casinos by a detective agency. Along with the humiliation of having their photos next to hustlers and pickpockets, this notoriety made it nearly impossible for them to continue playing in Vegas. They needed a new venue.
Woods was aware of large horse-betting pools in Asia, with the biggest being run by the Hong Kong Jockey Club. Established in 1884 as a sanctuary for upper-class Brits seeking a piece of England in their subtropical colony, the club evolved into a state gambling monopoly. Its two courses, Happy Valley and Sha Tin, were packed twice a week during the racing season, which ran from September to July. Despite Hong Kong's population being only about 5.5 million at the time, it bet more on horses than the entire U.S., with annual wagers reaching around $10 billion by the 1990s.
Hong Kong racing employs a parimutuel system, also known as a "totaliser." Unlike the fixed odds in a Vegas sportsbook, which favour the house, parimutuel odds adjust fluidly based on how bettors place their wagers. Winners share the pool, with the house taking a commission of around 17 per cent. (After expenses, the Jockey Club’s proceeds go to charity and the state, contributing up to a tenth of Hong Kong’s tax revenue.) To profit, Benter had to make bets that exceeded the club’s 17 per cent cut.
Benter visited the Gambler’s Book Club in Vegas and purchased everything available on horse racing. Many “systems” promised great results but seemed flimsy, often written by journalists and amateur handicappers with little mathematical basis. Seeking something more rigorous, Benter went to the University of Nevada at Las Vegas library, known for its gaming collection. Among stacks of periodicals and manuscripts, he found an academic paper titled “Searching for Positive Returns at the Track: A Multinomial Logit Model for Handicapping Horse Races.” He read it thoroughly, twice.
The paper suggested that a horse's performance could be quantified probabilistically using variables such as speed, size, win records, and jockey skill. By weighting these variables, one could predict a horse's chances. More and better variables and finer weightings improved the predictions. The authors, however, needed to be more certain about the strategy's profitability and focused on statistical models without testing the theory thoroughly. They concluded that there was some optimism.
Benter taught himself advanced statistics and learned to write software on an early PC. In the fall of 1984, Woods travelled to Hong Kong and sent back yearbooks containing thousands of race results. Benter hired two women to manually enter the data into a database, allowing him to focus on studying regressions and developing code. After nine months, in September 1985, he flew to Hong Kong with three bulky IBM computers in his checked luggage.
Hong Kong, a booming financial hub with some of the world's most densely populated areas, greeted Benter. The city's crowded skyline, which had inspired Ridley Scott’s dystopian vision in Blade Runner, seemed to grow daily.
Benter and Woods rented a tiny apartment in a run-down high-rise. Cantonese music drifted through the stained walls, and neighbours shouted in the hallways all night. Their office consisted of an old desk and a wooden table piled high with racing newspapers. Their rare outings were to the nearby McDonald’s.
Working on Improving his System
Twice a week on race days, Benter would sit at the computer while Woods studied the racing form. Initially, Benter's betting program produced odd predictions, which Woods, having spent a year studying the Hong Kong tracks, would adjust. They placed their bets through a telephone account with the Jockey Club and watched the races on TV. When they won, they only allowed themselves satisfied smiles; as professionals, they avoided overt celebrations.
Between races, Benter worked to ensure his algorithms could overcome a statistical challenge known as gambler’s ruin. This concept suggests that a player with limited funds, continuously betting against an opponent with unlimited resources (like a casino or the betting population of Hong Kong), will eventually go broke, even in a fair game. All winning streaks end, and losing streaks can be disastrous.
To address this, Benter drew on strategies from his blackjack days, particularly the work of a Texas physicist named John Kelly Jr., who tackled this issue in the 1950s. Kelly proposed a scenario where a horse-racing gambler has an edge, such as fairly reliable tips. The key was determining how much to bet: too little wastes the advantage, while too much risks ruin, given that the tips are not infallible. Kelly’s solution was to bet an amount proportional to the gambler’s confidence in the tip.
Benter noticed the parallels between Kelly’s hypothetical tip wire and his own prediction software. Both were essentially private systems that provided slightly more accurate odds than the public ones. For instance, if the public could bet on a horse at 4 to 1 odds, Benter’s model might indicate that the horse has a one in three chance of winning. This allows Benter to risk less for the same return, turning a small edge into a significant profit. Additionally, betting thousands of times helps mitigate the impact of bad luck. Kelly’s equations, when applied to the large-scale betting enabled by computer modelling, seemed to promise success.
However, this depended on the accuracy of the model. By the end of their first season in Hong Kong in the summer of 1986, Benter and Woods had lost $120,000 of their $150,000 stake. Benter returned to Vegas to seek investment but failed, while Woods went to South Korea to gamble. They reconvened in Hong Kong in September. Woods, having more money than Benter, was willing to recapitalise their partnership—under one condition.
“I want a larger share,” Woods stated, according to Benter.
“How much larger?” Benter asked.
“Ninety per cent,” Woods replied.
“That’s unacceptable,” Benter responded.