blackjack

On Gambler’s Fallacy in Blackjack

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Jonathan Adler has penned an excellent guest post on Felix Salmon’s blog regarding the gambler’s fallacy when playing blackjack:

Blackjack is a game where it is easy to fall prey to the gambler’s fallacy. As a player, if you receive several losing hands in a row it is easy to think that you’re “due” for a winning hand. However since each hand is essentially an independent event (and I’ll get back to this later), the number of losses you have had in a row doesn’t change chance of you getting a win on your next hand. Even if you get a run of bad hands in a row, your next hand is still just about as likely to lose as the previous one, similar to the situation with flipping a coin.

Adler then recounts the story of hedge fund manager Michael Geismar and how he was able to work with a different gambling strategy:

Lawrence Delevingne’s story on Michael Geismar’s time in Vegas is a great anecdote showing that people in charge of billions of dollars on Wall Street don’t understand the idea of shifting risk. After hearing Ben Mizrech speak, Geismar was seen using a betting strategy to try and improve his winnings at the blackjack table. After every winning hand, he would increase his bet by $1,000. After a losing hand he would lower his bet. The article doesn’t say by how much, but let’s assume after losing a hand he would reset his bet to $1,000.

This betting strategy has the opposite effect the one described before; instead of having a single win wipe out previous losses, a single loss will wipe out much of the earlier winnings. On most sequences of hands Geismar would lose money, but occasionally he will have an unlikely winning streak and make a very large amount. Instead of shifting the downside risk to the tail events, Geismar shifted the upside risk to tail events. Over time this betting strategy is expected to lose Geismar money, just like all other betting strategies. But Geismar fell victim to the gambler’s fallacy: he thought that a run of winnings changed the chance of getting another winning hand.

The takeaway is this: any kind of gambling strategy that you devise will not work against the house in the long run. Card counting can give you an edge, but it’s extremely difficult to put into practice.

I myself have been prone to devise gambling strategies when playing blackjack, and reading Adler’s post serves as affirmation that doing so doesn’t work. That interlude of Geismar’s lucky streak is just a major deviation, a long tail event.

The Man Who Broke Atlantic City

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Don Johnson won almost $6 million playing blackjack in one night, single-handedly obliterating the monthly revenue of Atlantic City’s Tropicana casino. Not long before that, he’d taken the Borgata for $5 million and Caesars for $4 million. But Don Johnson isn’t a card counter. So how did he do it?

Turns out, he is one of those sophisticated (high roller) gamblers who can negotiate with casinos, as explained in this story in The Atlantic:

Sophisticated gamblers won’t play by the standard rules. They negotiate. Because the casino values high rollers more than the average customer, it is willing to lessen its edge for them. It does this primarily by offering discounts, or “loss rebates.” When a casino offers a discount of, say, 10 percent, that means if the player loses $100,000 at the blackjack table, he has to pay only $90,000. Beyond the usual high-roller perks, the casino might also sweeten the deal by staking the player a significant amount up front, offering thousands of dollars in free chips, just to get the ball rolling. But even in that scenario, Johnson won’t play. By his reckoning, a few thousand in free chips plus a standard 10 percent discount just means that the casino is going to end up with slightly less of the player’s money after a few hours of play. The player still loses.

But two years ago, Johnson says, the casinos started getting desperate. With their table-game revenues tanking and the number of whales diminishing, casino marketers began to compete more aggressively for the big spenders. After all, one high roller who has a bad night can determine whether a casino’s table games finish a month in the red or in the black. Inside the casinos, this heightened the natural tension between the marketers, who are always pushing to sweeten the discounts, and the gaming managers, who want to maximize the house’s statistical edge. But month after month of declining revenues strengthened the marketers’ position. By late 2010, the discounts at some of the strapped Atlantic City casinos began creeping upward, as high as 20 percent.

The house has advantage, over long term, with typical gamblers who wager from a few to a few hundred dollars per hand. But when you have elite status and can negotiate with casinos to give you discounts on losses, you can turn the odds in your favor. And that’s what Don Johnson did…

Last question: is Don Johnson the most famous blackjack player in the world? That’s what the article attests.