Inverse Gambler's Fallacy

Let's continue with discussion of the gambler's fallacies that we began a few weeks ago.

You may recall that the first fallacy we spoke about was that "the odds have to even out." That is, in slot terms, if we've been getting a lot of losing spins during a certain period, we're due to have a hot streak because the machine isn't supposed to be so stingy. Or the reverse--if we're on a hot streak, the machine is due to turn cold because the casino isn't going to fund our retirement with our winnings from this machine.

In general terms, this gambler's fallacy is that something that has been happening a lot in the past is less likely to happen in the future and something that hasn't been happening in the past is more likely to happen in the future.

While researching the gambler's fallacy, I discovered that there are many gambler's fallacies. This one is called the "inverse gambler's fallacy."

Why is it called the "inverse gambler's fallacy?" What's an "inverse gambler?" Someone who never goes to a casino and invests only in bank CDs? That poor joke aside, I'll explain why it's called the inverse gambler's fallacy a bit later. For now, here's an example of it:

You walk up to a craps table and you see the shooter roll a 12. You have no idea how long he's been shooting, but you figure that he must have been shooting for a while because 12 is one of the two rarest rolls.

A slot example: You see someone who hit the jackpot on a slot machine. You figure that person was probably playing for quite a while because the jackpot hits so infrequently.

In the first fallacy we looked at, we were trying to guess what would happen in the future based on what has happened in the past. In this fallacy, we're making a prediction on what has happened in the past based on the present. That's why it's the inverse gambler's fallacy--we're guessing about the past instead of the future.

Now, here's an illustration of this fallacy in action that you see every day in the casino: When players hit the jackpot or a royal flush, the casino asks them to play off the jackpot. Some casinos in the past would even give you the money to play off the jackpot and you could keep any winnings.

Why do they want you to play off the jackpot? Because some players won't play a machine that shows a jackpot. They figure that jackpot hits are separated by many, many spins so they'll let someone else play this machine. They figure that a machine that doesn't show the jackpot is closer to hitting again.

The truth is that the odds for hitting the jackpot are the same on every spin. It doesn't matter if the last spin resulted in three blanks, three cherries, or three Megabucks symbols and it doesn't matter how long it's been since the jackpot last hit. The odds don't change.