Aside from his dancing left foot, Anthony Curtis, 42, looks like any other sucker tourist dropping a wad at the Binion’s Horseshoe blackjack tables in Las Vegas.
Hair slicked back, nose busted twice from rugby, left hand curled around his second imported beer–not water, a dead giveaway for card counters–he seems wound tighter than most, maybe, but inside the bounds. After three minutes of play, he’s down $100. He seems distracted by the waitress’ cleavage and acts surprised when his luck turns.
“My God, this never happens,” he murmurs as he flips a natural 21: a 10 of hearts and ace of diamonds. Next two hands, he stands on 17 and 18. The dealer busts both times. Now he’s up $150–“Better quit,” he says, clumsily scooping up 12 green chips and striding to the cashout cage. The pit boss–whose job it is to spot counters–smiles and waves at him. The dealer doesn’t even look up.
While Curtis did his dumb-luck shtick above the table, the real action was below, down on the gaudy carpet. One of the best blackjack players in the world–he won the World Match-Play Blackjack Championship in 1987–Curtis counted every card played, maintaining a multiparameter tally, which means he tracked several things at once.
His left foot’s job was to tick off the aces. When one ace had been dealt, he put his heel down; second ace, he tilted his foot to the left; third, up on his toe; fourth, tilted to the right. Meanwhile, in his head, he kept a running count of the other cards: Twos and eights each counted as plus one; threes, fours, sixes and sevens were each plus two; fives were plus three; nines were minus one; and 10s and face cards (which all count as 10 in blackjack) were minus three.
The idea is that blackjack–unlike, say, craps–is a game of dependent events, and tracking the dealt cards yields valuable information about the ones that remain. A wealth of 10s and aces left in the deck favors the player, because the player is more likely to get a blackjack (for which the house pays 1.5 times the bet) and because the house, which plays by fixed rules, is more likely to bust. Whenever Curtis’ count went positive–that is, above zero–he boosted his average bets and, on this evening, his winnings.
Do it all while looking like a distracted, none-too-bright vacationing drunk, and you, too, can win big. Card counting can be daunting–it’s a science that’s under constant revision and an art that demands great discipline–but it can also be extremely rewarding. By 1989 Curtis had won enough money at the tables to bankroll a gambling-book publishing house. He still plays in his off hours and remains plugged into the professional blackjack subculture.
Standing shoulder to shoulder with the hapless hordes, Curtis represents the tiny coterie of mathematically talented, driven, inconspicuous gamblers who methodically drub the casinos at their own games. Even those who don’t plan to go pro can learn from the new gambling elite and turn a potentially impoverishing vacation into a profitable experience.
“To figure this stuff out is just very alluring to someone like me,” says Olaf Vancura, a casino-game creator with a PhD in physics and the author of “Knock-Out Blackjack,” a new card-counting system that’s within the reach of the average intellect. Winning over the long haul demands research, stamina, nerve and no small measure of acting ability, but the principal requisite is a rock-solid grounding in probability.
Curtis estimates that 99 percent of what’s offered in casinos and other legal betting venues is what he terms negative expectation games, meaning that over the long haul, the house will harvest anywhere from 1 percent to 60 percent of money gambled. The average bettor accepts his skinning because he imagines the house odds are insurmountable. The average bettor is wrong.
“People always say, `Who pays for the lights in Las Vegas?'” observes Jean Scott, a 61-year-old video-poker-playing grandmother who, with her husband, Brad, earned enough in two years to purchase their Las Vegas condo. “All I know is, I don’t.”
The books that inspired Curtis grew out of a flowering of scientific gambling analysis that began with “The Optimum Strategy in Blackjack,” an article printed in 1956 in the Journal of the American Statistical Association. Four Army mathematicians, known today as the Baldwin group, demonstrated how to play each hand to maximize winning potential, proving that a player who followed their program in a single-deck game would, over time, be virtually even with the house.
That made blackjack by far the most advantageous casino game to play. But the giant of blackjack theory, and nearly a god to young Curtis, was MIT mathematics professor Edward O. Thorp, who published “Beat the Dealer” in 1962.
The Baldwin group had focused on how to optimize play using each hand’s visible cards, reckoning that card counting was impractical. Thorp’s twin breakthroughs, bolstered by then-nascent computer calculation, were that smart folks could learn to count cards as they were played and that, in doing so, these gamblers could gain a consistent advantage over the house.
On his own, day after day, Curtis practiced card counting until his brain ached and his fingers were raw. At 21, he turned his back on a UCLA wrestling scholarship, moved to Las Vegas, bellied up to the Sahara’s blackjack pit and put his $1,800 life’s savings on the line.
“The first night, I won $22,” he says. “The second day, I lost $900. At the table, I started hyperventilating. Then I got physically sick.”
Curtis had slammed into the brutal reality of fluctuation around the average return, or what statisticians call standard deviation. Although an astute blackjack card counter can, over the long haul, realize up to a 1.5 percent profit (depending on such variables as the number of decks, which card-counting system he employs and how many cards remain before the dealer reshuffles), losing streaks can last for weeks.
There’s a saying: If you can’t stand the flux, don’t bet the bucks. Many technically proficient blackjack counters have been run out by flux. An elegant mathematical expression of standard deviation’s power in gaming is the so-called risk of ruin, which establishes the likelihood that a particular bankroll will go to zero before it doubles.
According to calculations by Vancura, a blackjack card counter playing with a 101.11 percent expected return (the expectation of one version of his card-counting system) and a bankroll that’s just 25 times the minimum bet has close to a 47 percent chance of going broke before doubling his money. To drop the likelihood of going broke to, say, 0.5 percent requires a bankroll 1,000 times larger than the game’s minimum wager; in a $5 to $25 game, that’s $5,000.
Chastened, Curtis returned to the real world, first as a stockbroker, then as the smallest bouncer in Las Vegas. The lean years ended when Stanford Wong–the nom de guerre of a statistics and finance professor who relishes anonymity–enlisted Curtis to play tournament blackjack. Financed by Wong, Curtis was free to make the big bets that would harvest big money.
After he retired from tournament play, Curtis set up his publishing house. Today, he reigns over a stable of authors in his growing library of gambling science.
But even if Vancura’s simplified card-counting book achieves best-seller status, as Thorp’s did, the lights will likely keep blazing just as fiercely in the desert and along the boardwalk and in the Indian casinos and on the riverboats and aboard the ocean liners: Curtis and Vancura seem appalled at the apathy and ignorance of the average gambler.
Successful gambling is unquestionably possible, and someday, they hope, the fleeced hordes will decide they’ve lost enough. Someday casino profits may shrink from the obscene to the merely respectable, and the successes of those who win through intellectual effort rather than luck may inspire a newfound appreciation for the beauty, wonder and irresistible power of probability.
But don’t bet on it.
