Casino Strategy and the Gambler’s Fallacy

Casino Strategy and the Gambler’s Fallacy

It can be very tempting to fall into superstitious habits when you’re in a casino. If you win every time you kiss your girlfriend or wear a lucky hat, you’re going to keep doing it – probably even after it stops working! For the most part, these little habits and beliefs aren’t very harmful, and might even make your casino visit more fun.

But there’s at least one commonly held belief that can actually hurt your chances at the casino, especially if you buy into a casino strategy that revolves around it. It’s called the gambler’s fallacy, and it’s something everyone falls into at least once in their casino career.

Have you ever been at a roulette table where red has come up six or seven times in a row, and bet on black because you’re sure it’s due? If so, then you’ve committed the gambler’s fallacy by assuming previous results will influence the next completely independent event that’s about to happen. The roulette wheel has absolutely no memory of its previous spins, so there’s no reason to believe that the very next spin will “correct” the run of red.

This sometimes takes people by surprise, because they also believe that the “law of averages” or the “law of large numbers” dictates that things need to balance out in the end, since we know that in the long run, the results we see will closely mirror the probability of each individual event. The problem is that in the long run, the results will approach what probability predicts, but there’s no guarantee that those results will come out to the exact percentages we expect. In the long run, that little streak of red we saw will barely effect the overall percentage of times red has come out on that roulette wheel, especially if we tracked the wheel’s results over a few days, weeks or months.

Here’s an example. Let’s say we flip a coin ten times, and get heads all ten times. Right now, the results stand at 100% heads, while probability tells us we should only have 50% heads. However, we don’t need a run of tails to “fix” this! If the next 1,000 flips simply come out at a 50/50 rate between heads and tails, those first 10 flips will barely seem like a drop in the bucket. At this point, heads has now shown up 50.5% of the time. If we have another million flips with the expected 50/50 results, then we won’t be able to tell there was even a run of heads at all.

The gambler’s fallacy won’t hurt you in a game like roulette; since all the bets have the same house edge anyway, it doesn’t matter if you bet on red or black in the long run. But in other games, like craps, the gambler’s fallacy can often lead people to bet on things that carry a high house edge simply because they mistakenly believe these bets are due to hit. Even worse, believing in the gambler’s fallacy can lead a player to put faith in betting systems that rely on events happening simply because they haven’t in a long time. By the time these players realize they’ve been duped, they may already have lost a lot of money.

It’s important to point out that the gambler’s fallacy doesn’t apply when the events aren’t independent, such as when you’re counting cards in blackjack. In this case, the results of earlier hands actually do change the odds for future hands, so it’s not a fallacy to bet more when the numbers are in your favor. But in most cases, you should stick to basic gambling strategies, and avoid bad bets that are only being made because they feel overdue.