Right Attitudes

The Gambler’s Fallacy is the misleading belief that the probability of a specific occurrence in a random sequence is dependent on preceding events—that its probability will increase with each successive occasion on which it fails to occur.

Suppose that you roll a fair die 14 times and don’t get a six even once. According to the Gambler’s Fallacy, a six is “long overdue.” Thus, it must be a good wager for the 15th roll of the dice. This conjecture is irrational; the probability of a six is the same as for every other roll of the dice: that is, 1/6.

Chance Events Don’t Have Memories

In practical terms, the Gambler’s Fallacy is the hunch that if you play long enough, you will eventually win. For example, if you toss a fair coin and flip heads five times in a row, the Gambler’s Fallacy suggests that the next toss may well flip a tail because it is “due.” In actuality, the results of previous coin flips have no bearing on future coin flips. Therefore, it is poor reasoning to assume that the probability of flipping tails on the next coin-toss is better than one-half.

A classic example of the Gambler’s Fallacy is when parents who’ve had children of the same sex anticipate that their next child ought to be of the opposite sex. The French mathematician Pierre-Simon Laplace (1749–1827) was the first to document the Gambler’s Fallacy. In Philosophical Essay on Probabilities (1796,) Laplace identified an instance of expectant fathers trying to predict the probability of having sons. These men assumed that the ratio of boys to girls born must be fifty-fifty. If adjacent villages had high male birth rates in the recent past, they could predict more birth of girls in their own village.

There Isn’t a Lady Luck or an “Invisible Hand” in Charge of Your Game

The Gambler’s Fallacy is what makes gambling so addictive. Gamblers normally think that gambling is an intrinsically fair-minded system in which any losses they’ll incur will eventually be corrected by a winning streak.

In buying lottery tickets, as in gambling, perseverance will not pay. However, human nature is such that gamblers have an irrational hunch that if they keep playing, they will eventually win, even if the odds of winning a lottery are remote. However, the odds of winning the jackpot remain unchanged … every time people buy lottery tickets. Playing week after week doesn’t change their chances. What’s more, the odds remain the same even for people who have previously won the lottery.

Gambler’s Fallacy Coaxed People to Lose Millions in Monte Carlo in 1913

The Gambler’s Fallacy is also called the Monte Carlo Fallacy because of an extraordinary event that happened in the renowned Monte Carlo Casino in the Principality of Monaco.

On 18-August-1913, black fell 26 times in a row at a roulette table. Seeing that that the roulette ball had fallen on black for quite some time, gamblers kept pushing more money onto the table assuming that, after the sequence of blacks, a red was “due” at each subsequent spin of the roulette wheel. The sequence of blacks that occurred that night is an unusual statistical occurrence, but it is still among the possibilities, as is any other sequence of red or black. As you may guess, gamblers at that roulette table lost millions of francs that night.

Gambler’s Fallacy is The False Assumption That Probability is Affected by Past Events

The Gambler’s Fallacy is frequently in force in casual judgments, casinos, sporting events, and, alas, in everyday business and personal decision-making. This common fallacy is manifest by the belief that a random event is more likely to occur because it has not happened for a time (or a random event is less likely to occur because it recently happened.)

• While growing up in India, I often heard farmers discuss rainwater observing that, if the season’s rainfall was below average, they worry about protecting their crops during imminent protracted rains because the rainfall needs to “catch-up to a seasonal average.”
• In soccer / football, kickers and goalkeepers are frequently prone to the Gambler’s Fallacy during penalty shootouts. For instance, after a series of three kicks in the same direction, goalkeepers are more likely to dive in the opposite direction at the fourth kick.
• In the episode “Stress Relief” of the fifth season of the American TV series The Office, when the character Jim Halpert learns that his fiancee Pam Beesley’s parents are divorcing, he quotes the common statistic that 50% of marriages wind up in divorce. Halpert then comments that, because his parents are not divorced, it is only reasonable that Pam’s parents are getting divorced.

The Gambler’s Fallacy is a Powerful and Seductive Illusion of Control Over Events That are Not Controllable

Don’t be misled by the Gambler’s Fallacy. Be aware of the certainty of statistical independence. The occurrence of one random event has no statistical bearing upon the occurrence of the other random event. In other words, the probability of the occurrence of a random event is never influenced by a previous, or series of previous, arbitrary events.

Idea for Impact: Be skeptical of most judgments about probabilities. Never rely exclusively on your intuitive sense in evaluating probable events. In general, relying exclusively on your gut feeling or your hunches in assessing probabilities is usually not a reason to trust the assessment, but to distrust it.