At The Monte Carlo Casino On August 18, 1913, Patrons Witnessed A 1 in 67 Million Event, And Lost Millions In The Process

First up, what is the gambler's fallacy? Imagine you are playing a game tossing coins, perhaps with Rosencrantz and Guildenstern. You toss the coin, and it turns up heads. You toss it again, and once more you are met with a big old head. 

You keep flipping the coin, and the coin keeps on turning up heads, 20 times in a row. The odds against that are 1 in 1,048,576. 

So, what are the odds of the next coin toss being tails? The answer, of course, is 1 in 2, or 50/50 (or slightly off that if you really want to be a pedant about it). Each coin toss is independent of the last coin toss, and the results of those previous tosses has no effect on the result of the next coin toss. 

The gambler's fallacy is to believe that the previous independent results have any bearing on the next independent result, for instance believing that a tails outcome is now more likely because of all the previous heads.

An excellent example of this fallacy was taught the hard way to gamblers at the Casino de Monte-Carlo in Monaco, back in 1913. 

On that night in August, patrons at the roulette table watched as the ball swirled around the wheel, and landed on black an astonishing 26 times in a row. The odds of this happening are around 1 in 1/67,108,865, making it an extremely unlikely event for you yourself to witness. 

It was an extremely unlikely event for those particular witnesses on that particular night, but that doesn't mean it was an unlikely event for humanity and gamblers as a whole.

While you personally should not expect to witness something like this, you should expect somebody somewhere to experience extraordinarily unlikely events like it. Essentially, there are enough roulette tables and coin tosses, that someone out there will hit a streak. As statistician David J. Hand put it, "extremely improbable events are commonplace."

"With a large enough sample, any outrageous thing is likely to happen," a paper on coincidences explains. "The point is that truly rare events, say events that occur only once in a million are bound to be plentiful in a population of 250 million people. If a coincidence occurs to one person in a million each day, then we expect 250 occurrences a day and close to 100,000 such occurrences a year."

Gamblers at the Casino de Monte-Carlo were clearly unaware of the fallacy they were about to fall face first into. As the streak of blacks grew longer, patrons began to bet heavily on red, apparently under the belief that all the previous black results meant that red was more likely to pop up next.

According to the BBC, people lost millions of Monégasque francs in the rush to bet on red, despite the continuing 50/50 odds. The lesson? If you're going to gamble, pay a little more attention to probability. Unfortunately, it is probably too late to win the lottery using some incredibly basic math.