The Gambler’s Guide to Winning

Hint: you can’t.

On August 18, 1913, gamblers at the Monte Carlo Casino witnessed what seemed like a mathematical impossibility. The ball at the roulette table landed on black an astonishing 26 times in a row! This phenomenon, dubbed the Monte Carlo fallacy or the gambler’s fallacy, represents the battle between intuition and the cold logic of probability.

The gambler’s fallacy is the belief that if something happens more than usual, it will happen less frequently in the future. In the case of roulette, each spin is an independent event, as the wheel has no memory of its own. Yet people think that a streak must “even out” soon.

Assuming the table was a standard European roulette table (containing 18 red pockets, 18 black pockets, and one green pocket), and the table was completely unbiased, the chance for the wheel landing on black 26 times would be around 0.000000026% or 1 in 38 million. Faced with such an unlikely streak, many of the gamblers assumed the wheel had to land on red next.

Consequently, the fallacy preys on our brain’s craving for equality and balance, causing a mental bias toward the other event. In other words, our brain has a tendency to search for order in chaos. Humans are pattern-seeking creatures, so when the randomness fails to look “fair,” we instinctively expect a correction. This is known as the “law of small numbers,” in which people believe that short sequences must reflect long-term averages.

Here are some examples of the law in play:

Coin toss: Imagine tossing a coin 100 times. Even though the long-term average is about 50 heads and 50 tails, small streaks (like 10 heads in a row) happen more often than people expect.

Basketball shots: Fans sometimes believe that a player who misses several shots is “due” for a basket, or that a player on a streak “can’t miss.” However, each shot is fully dependent on skill and chance.

Lottery tickets: Some people think that a number that has not “come up in a while” is therefore “due.” However, each draw is equally random.

When we apply these concepts back to gambling, the picture becomes clear: games of chance are built to take advantage of these mental biases. Slot machines, roulette tables, and even video game loot boxes are engineered to give you the illusion of control, when in reality, the house always wins.

Improving your ability to understand statistical information can be an effective way to mitigate the effects of the gambler’s fallacy. Knowing the nature of true randomness can help us avoid falling into this mental trap. The Monte Carlo incident of 1913 remains a timeless reminder that randomness does not play fair; it plays random.