Gambler's fallacy

Simulation of coin tosses: Each frame, a coin is flipped which is red on one side and blue on the other. The result of each flip is added as a colored dot in the corresponding column. As the pie chart shows, the proportion of red versus blue approaches 50-50. The difference between red and blue dots is never zero.

The term Gambler's fallacy refers to a misconception about statistics. It is also known Monte Carlo fallacy or fallacy of the maturity of chances. In statistics, a random event has a certain probability of occurring. The fallacy is that if the event has occurred more frequently in the past, it will occur less frequently in the future; or that if it has been less frequent in the past, it will be more frequent in the future.

Childbirth

As early as 1796, the idea of the gambler's fallacy was used to "predict" the sex of children. In his work A Philosophical Essay on Probabilities, published in 1796, Pierre-Simon Laplace wrote of the ways in which men calculated their probability of having sons:"I have seen men [who wanted to have] a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls." In short, the expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter.

Some expectant parents believe that, after having multiple children of the same sex, they are "due" to have a child of the opposite sex. While the Trivers–Willard hypothesis predicts that birth sex is dependent on living conditions (i.e. more male children are born in "good" living conditions, while more female children are born in poorer living conditions), the probability of having a child of either sex is still generally regarded as near 50%.