The gambler’s fallacy, which is also known as “the fallacy of the maturity of chances” or the Monte Carlo fallacy, is a false assumption that whenever some random event occurs frequently over some time period, it is less likely to occur in the near future. The reasons why this line of thinking is so popular among the less experienced gamblers are fairly simple: most people are prone to assume that every small streak must eventually even out in order to keep the action in balance and fair.
This kind of assumption gives the player a false sense of control over the flow of the game, allowing him to believe that he can predict the course of events. Unfortunately, this belief is invariably false, as subsequent random events don’t stop being random because of previous outcomes.
In order to illustrate this point, let’s consider a simplified game of Roulette with no 0 or 00 fields on the wheel. In such a case, the probability of the ball landing on a Red field is exactly 1/2, which means that the probability of winning two subsequent Red bets is 1/4, while the probability of winning three subsequent Red bets is 1/8.
After winning two subsequent Red bets, a person falling back on the gambler’s fallacy will generally assume that the outcome of the third game is more likely to be Black than Red, because the probability of winning three subsequent Red bets is only 1/8. However, at this point the probability of winning that bet is 1/2, because the previous outcomes are no longer unknown, which means that their probabilities are 1. While a streak of three Red wins indeed has a chance of 1/8, this is true only before the first of three balls is tossed onto the Roulette wheel.
The reason why gambler’s fallacy is so dangerous is that it may lead players to relying on betting systems that increase their chance of ruin, such as the Martingale. In this betting system, the player is required to double his bet after every loss, particularly when placing even money wagers such as Red or Black in Roulette and Pass or Don’t Pass in Craps. The gambler utilizing the Martingale assumes that this allows him to cover all of his past losses and gain one unit.
For example, if the opening bet is $1 and the player loses three bets in a row, the total losses will equal $1+$2+$4 = $7. Consequently, winning on the fourth game allows the player to win $8 and profit $1. Unfortunately, the possibility of suffering a string of defeats that will deprive you of your money in total is very real and in fact quite likely once you reach wagers that you can hardly afford.
The truth is that regardless of the system you use, the ratio of money lost to money wagered will always be close to the normal house advantage. The only difference between playing the Martingale and betting flat is in fact the speed at which you accelerate your game, which means that you’re quite likely to run out of money significantly faster and that you won’t be able to enjoy yourself at the tables as much as you normally would.
There are many dishonest people that take advantage of the gambler’s fallacy to sell their betting systems – if you ever stumble onto a site advertising for an offer of this kind, you should definitely give it a pass and take everything written there with a grain of salt.