On Gambler’s Fallacy in Blackjack

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.

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