Imagine yourself in a Las Vegas casino waiting patiently to play the slot machines. All of a sudden someone “hits” the jackpot. That person, along with her friend, leaves to spend her newly won fortune. There are now two slot machines available. Which machine would you choose to play, the one used by the woman who just hit the jackpot, or the one used by her friend? Why?
Having no luck playing the slot machines you wander over to a roulette table. You decide to play it safe by betting only on whether the number that comes up is red or black. (18 of the 38 numbers on a roulette wheel are red and 18 are black.) As you get ready to place your bet the man standing next to you advices that you better bet on red since the last five spins of the wheel have resulted in a black number. He says, “ the wheel is due for a red. “ Should you follow his advice and bet red? Why or why not?
Assuming that the slot machine is fair, any two plays of the slot machine constitute a pair of independent events. Similarly any two spins of a fair roulette wheel are independent. Thus, knowing that a slot machine has just paid a jackpot has no influence on the probability of it paying a jackpot in the future. Similarly, the fact that the roulette wheel has come up black five times in a row has no influence on the probability of which color number will subsequently appear. The probability that the roulette wheel will show a black number six consecutive times is (18/38)6 ~ .0113, but the probability that the roulette wheel will show a black number, given that it has previously shown 5 consecutive black numbers, is 18/38. It does not matter which slot machine you choose or which color you bet on, the probability of winning will be the same.
The common belief that a particular outcome is “due” to happen, (or not to happen) based on the outcomes of previous experiments is known as the “Gambler’s Fallacy.” The Gambler’s Fallacy was a major contributor to the more than nine billion dollars in gambling revenue taken in by the Nevada casinos in 2001.