Now what if he flipped the coin nine times and it came up heads every time? For the tenth flip, would you give him the same 1,000-to-1 against heads? If you were to do so, it would be a big mistake, and this mistake is the cornerstone of the gambler’s fallacy.

The Principle of the Gambler’s Fallacy

The gambler’s fallacy is the idea that previous trials affect the odds of a random event. In the above example, the fact that heads showed up nine times in a row has absolutely no bearing on whether the coin will come up heads the tenth time.

Once the nine have already happened, the odds of the tenth flip coming up heads are 50-50, just like the first flip. The coin has no memory and you might as well be flipping it the first time, or be flipping a different coin.

How the Gambler’s Fallacy Affects Casino Gambling

The gambler’s fallacy has a big role in casino gambling. People who gamble tend to look for patterns in the hope of getting an edge on the game.

If they notice that black has come up on a roulette wheel many times in a row, they may be more likely to bet red. If they have lost spins of roulette in a row, they may double their bets, assuming that the odds of winning are better.

This is in fact the basis for the fallacious Martingale System, in which a player doubles his bet after every loss. In the short term, losses can occur many times in a row without altering the game in some way. Gamblers who do not believe this can find themselves in serious problems if they base their betting on this belief.

Notes on the Gambler’s Fallacy

It’s important to know that this belief is a fallacy only in the case of events with replacement, in which the conditions are the same in each trial. In a game like blackjack, in which certain cards are not replaced right away, prior events can affect future events, and this is in fact the fundamental basis of card counting.