The Gambler's Fallacy

© Håkan Dahlström (Flickr) Roulette wheel
© Håkan Dahlström (Flickr)

If you are playing roulette and the ball falls on black eighteen times in a row, how do you bet? If you choose to bet on red because you think it is due, this is the Gambler’s Fallacy.

In fact, with any fair gambling game, every new hand should be perceived as a separate event, with the likelihood of results unchanged.

Logic
Being black once does not give the wheel more weight to be red the next turn, so falling black eighteen times will have equally little effect on the next spin.

Runs of luck, or misfortune, will occur, but observing the aftermath of such a streak does not help us to predict the future.

Beliefs
The Gambler’s Fallacy can similarly represent the belief that a losing streak must inevitably end, that when you have lost a lot you are due to win. This is the fundamental belief that ruins many a gambler, as they press on to lose even more money when they are down.

What really happens?
In fact, pursuing a win after a succession of losses is, if anything, likely to compound your losses: a losing player is all too often an upset player, an upset player is all too often a bad player, and a snowball effect can be achieved.

A historical case
In the Monte Carlo Casino, 1913, a historic example of the fallacy occurred (hence the Gambler’s Fallacy is also sometimes called The Monte Carlo Fallacy). A roulette ball fell black 26 times in a row. After approximately
15 black results, gamblers rushed to place bets on red, believing it was surely due. By the time the tide finally changed, people had lost millions of francs in bets.

Sequences
The man who bet on the 27th spin may be forgiven for the coincidence of his success, but those who believed it coming sooner were victims of seeing a pattern in what was actually a sequence of random results. Consider what is more likely: 26 black and 1 red, or 27 black. The answer is that all sequences are equally likely.