Those of you in my classes know I recently went to Las Vegas to do some gaming. It reminded me about a common mistake people make in assessing the probabilities of random events – called “the gambler’s fallacy”.

If you have ever played or seen a roulette wheel, it is very simple. There is a wheel with 38 numbered compartments, numbered 0, 00, and 1 – 36. The 0 and 00 are green, while 18 of the remaining numbers are black, and 18 are red. A ball is spun, and people bet on what number, or what color they think will occur.

In statistical jargon, we say that spins of the roulette wheel are independent events. The probability, say of the wheel landing on a red number, is the same for each spin, slightly less than 0.5 (actually 18/38). The result of the last spin of a roulette wheel has no bearing on any future spins. The roulette wheel has no memory. In fact, casinos have an incentive to ensure this.

Do all gamblers understand this? If you happen to be sitting at a roulette table after say, red, has come up 6 times in a row, do people go on calmly about their business? I can tell you from my personal experience the answer to this question is no. Some people think that black is “due” – or more technically, they think the probability of the next spin coming up black is larger than 18/38.

Those doing so are wrong – and are committing the gambler’s fallacy. There are still 18 black numbers on the wheel, 38 spaces, and are all equally likely to occur. Hence the probability that a black number will come up on the next spin is still 18/38, regardless of how many times red has come up. The wheel has no memory.

Could simple economics have told us the answer to whether or not people understand the gambler’s fallacy (without having to watch people gamble)?

Almost all of the roulette tables in casinos have an electronic board that displays the results of the last 10 or so spins. You see the number that came up and whether it was red or black.

If the casino management thought people understood that spins were independent, would it be profitable to spend money on these signs? Based on the fact that casinos do spend cash on these signs, what does this suggest happens about how people change their bet (bet more, bet less) after 6 red spins show up on the roulette wheel?

–CT