If you flipped a coin in the air and got five heads in a row, would you feel like tail is due? If so, congratulations! You just experienced the gambler鈥檚 fallacy.
This thinking error comes about because we find it difficult to come to terms with the fact that random events are independent of one another. For example, at a large Reno, Nevada casino in 1998. They paid close attention to bets that were made that had odds of 50:50 (betting on a red number versus a black number, for example, or on an odd versus an even number). They noticed that bets overall were pretty much split down the middle, but as gamblers encountered streaks of five or more (e.g. five red numbers in a row), they significantly changed their bets (e.g. to a black number) as if it was due. But it wasn鈥檛. Whenever the ball is spun on the roulette wheel, it has no way of remembering where it landed before.
Each spin on the roulette wheel, each coin toss, each lottery ticket you buy is a beginning. It is not a continuation of a series of similar events. In the heat of the moment, however, it can be difficult to remember this lesson, and there are of course exceptions. Once a card is played in blackjack, it doesn鈥檛 immediately return to the deck, which means that the odds of receiving a certain card do change from hand to hand. And if you get 16 heads in a row when a friend flips a coin for you, you may suspect foul play.
But if you are dealing with a fair coin and no magnets, and you somehow end up getting 16 heads in a row, the odds of your next toss are still, incredibly, 50:50.
