The Calculus Diaries - Jennifer Ouellette [34]
Gambler’s ruin begins with the assumption—a false one, when it comes to craps—that the player has a slight advantage in a game of chance and should win slightly more than half the time. Say you have a bankroll of x dollars. For every dollar you bet, you win another dollar or lose the original dollar, depending on the outcome. (This is the same payoff rate as the pass and don’t-pass bets in craps.) What is the probability that you will run out of money, even with that slight advantage, rather than increase your bankroll by, say, doubling your money?
Drawing on that childhood fascination, Bacon devised a handy formula and plugged in a few values to see if a pattern emerged. He found that even with a fairly large advantage—say, 55/45—if you only start with $10 and make a fixed bet each time, there is an 11.8 percent chance of being ruined before you succeed in doubling your money. If you have a 51/49 advantage and a starting bankroll of $178, your chances of ruin before doubling up decrease to 0.1 percent, or 1 in 1,000. In craps, of course, you don’t have an advantage. Bacon has crunched those numbers, too. If the house has the usual edge of 1.42 percent, and you start with $100 and want to double it, your probability of ruin is 98.2 percent. That’s why casinos make such a killing.
So the first rule of gambling, for those who have studied the odds, is simply, Don’t.22 Still, craps is quite a lot of fun, provided you view it as harmless entertainment, rather than a get-rich-quick scheme to pad your 401(k). A good rule of thumb is to budget a set amount you are willing to lose and just chalk it up to the price of a day’s entertainment. Once you lose that amount, suck it up and walk away, and maybe explore a few of the other delights of Vegas.
Admittedly, this is easier said than done. For one thing, casinos employ a stickman at every craps table, whose job is to talk up the game and encourage players to make the riskier bets. For another, a 2008 paper in the Journal of Marketing Research reported on a study by two professors at the University of California. They found that even if people went into the casino determined to stay within their gambling budget, the pain of losing would usually cause them to bet more money in hopes of recouping their losses. Those who won tended to keep to their budget.
If someone develops a gambling addiction, the problem is even worse. In 2007, a Nebraska businessman named Terrance Watanabe lost nearly $127 million in a yearlong binge at the Caesars Palace and Rio casinos, blowing most of his personal fortune. When parent company Harrah’s Entertainment sued him for nonpayment of his gambling debt, Watanabe counter-sued, claiming casino staff plied him with drinks and encouraged him to gamble while intoxicated, thereby impairing his judgment. There could be an element of truth to that: High rollers like Watanabe—“whales” in the jargon of casino staff—are a lucrative source of income for casinos. As such, casinos treat them very well, doling out all manner of luxuries, free of charge, to keep them happy. But there are rules: Nevada gaming regulations stipulate that someone who is clearly intoxicated should not be allowed to gamble. In fact, Watanabe claimed he was barred from the Wynn casino for compulsive drinking and gambling; the Harrah’s establishments welcomed him with open arms.
Watanabe’s spectacular downfall is a rare occurrence. It is certainly possible to maximize your fun playing craps in a casino without breaking the bank. Just follow this basic principle: You want to play as long as possible with a fixed amount of money. That means losing as little as possible with each bet by choosing those bets with the most favorable odds and pay-outs. It’s easy to determine the optimal percentage of your bankroll you should bet in order to maximize your long-term return