Why Do We Fall for the Gambler’s Fallacy?

Why do we insist on believing that an event is due to happen? Luckily for casino owners, it seems almost impossible for the human brain to accept the fact that what happened to an inanimate object in the past has nothing to do with what will happen to it in the future.

I was a bartender for years and spent a lot of time around gambling machines. Electronic slot and poker machines were common in the places I worked and where I hung out. Most bartenders and bar owners would point out the machines that had not paid out for a while. The customers considered themselves blessed with this insider information. They were sure this would increase their chances of winning. They now knew what machine was due to pay out.

While this was good for business, the funny part was that most bar owners and bartenders believed the Gambler’s Fallacy too. Even though they were the ones who collected the money from the machines. They knew that the machine was programmed to allow a certain percentage of wins. These wins over time would average out to a certain fixed profit for the owner, say 20 percent. The machine was good at this, it didn’t make mistakes. Even if you play poker online, the accuracy is really high rated. 

But time meant nothing to the machine. It picked winners randomly. As long as it kept 20% out of 100%, it didn’t care if there were three winners in a row, three small winners over two days or one big winner in one day. The machine did not feel any pressure to give out a big win simply because it hadn’t done that lately.

The Gambler’s Fallacy is usually explained with coin tossing. That’s the easiest way to see how it works. Do you like to gamble? I’ll bet you $1000 to your $10 that you can’t flip 20 heads in a row. I know, you don’t like that bet. That would be too hard to do. So you don’t take the bet. But you give it a try anyway. Then you come running to me screaming, “Look, I just flipped heads 19 times in a row. I’ll take your bet now”.

But I know it’s the Gambler’s Fallacy saying that this would be the same bet. You’re saying that either way, you flipped 20 heads in a row. I’m saying that the bet is totally different and that you want 100 to 1 odds on a 50/50 chance. The bet that I first proposed was actually 20 separate bets. Heads twenty times in a row. Your new bet is one flip with even odds.

Neither the coin or the universe knows or cares how many heads have already been flipped. The odds do not change. They start over again at 50/50. The past does not influence the future.

Some people do make a living by gambling. They are not just lucky. They know the odds. They study the probabilities and don’t bet unless the odds are in their favor. The casinos and lotteries don’t make much money off of these people. They make their money off of chowder heads like us, who just can’t believe that even though that roulette wheel has come up black 10 times in a row, the odds haven’t changed. The odds are still against us. Red is not due.