# Gambler's fallacy

The gambler's fallacy is the logical fallacy of thinking that deviations from a long-term trend will be corrected in the short term.

Those who may believe a long-term trend is "overdue" to change often think that probability is on their side. They may believe that the probability of a specific event happening again is extremely low, because of how many times that event already happened.

For example, if a coin lands on heads multiple times in a row, one might think it is "overdue" to land on tails. In fact, the probability that a coin will land on just one side multiple times is (1/2)^n, where n is the number of flips. In 4 flips, there is only a 6% chance that it will land all heads. The gambler would look at this and may think another heads would be even more unlikely.

What the gambler and most others don't understand when playing gambling games is that each result is independent of the others. It's still a 50/50 chance that the next flip will be heads or tails.

A dependent event might be a result of choosing red or black randomly from a deck of cards when the cards are not replaced after each trial. At the beginning, red and black have an equal probability of being chosen. Say, though twelve black cards are chosen in a row. Now, there is a 35% chance of picking black on the third trial and a 65% chance of pulling red.

It is important to understand the difference between independent and dependent events in order to avoid this fallacy.

## Examples

• A person who is playing slot machines and has just lost ten times in a row may think that he is more likely to win on the next try.
• A person playing Roulette sees that red has come up repeatedly, so bets on black.
• Say a person lives in an area that has been hit by earthquakes every five years on average over the past 200 years. But it has been fifteen years since the last earthquake, so she assumes that the area is due for another one, perhaps of greater-than-usual severity.