“The simple maths error that can lead to bankruptcy”


That’s what the BBC calls the “gambler’s fallacy“, a widespread but mistaken belief in the odds of something happening.

Fifteen years ago, the people of Italy experienced a strange kind of mass hysteria known as “53 fever”.

The madness centred on the country’s lottery … Sometime in 2003 … the number 53 simply stopped coming up on the Venice wheel – leading punters to place increasingly big bets on the number in the certainty that it must soon make a reappearance.

By early 2005, 53 fever had apparently led thousands to their financial ruin, the pain of which resulted in a spate of suicides. The hysteria only died away when it finally came up in the 9 February draw, after 182 no-shows and four billion euros worth of bets.

While it may have appeared like a kind of madness, the victims had been led astray by a reasoning flaw called the “gambler’s fallacy” – a worryingly common error that can derail many of our professional decisions, from a goalkeeper’s responses to penalty shootouts in football to stock market investments and even judicial rulings on new asylum cases.

To find out if you fall for the gambler’s fallacy, imagine you are tossing a (fair) coin and you get the following sequence: Heads, Heads, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails. What’s the chance you will now get a heads?

Many people believe the odds change so that the sequence must somehow even out, increasing the chance of a heads on the subsequent goes. Somehow, it just feels inevitable that a heads will come next. But basic probability theory tells us that the events are statistically independent, meaning the odds are exactly the same on each flip. The chance of a heads is still 50% even if you’ve had 500 or 5,000 tails all in a row.

For the same reason, HTHTTH is just as likely as HHHHHH. Once again, however, many disagree and think that the mixed sequence is somehow more probable than the streak.

As its name suggests, the gambler’s fallacy has been of most interest to researchers studying games of chance. Indeed, it is sometimes known as Monte Carlo Fallacy, after a notorious event at one of Monaco’s roulette tables in 1913, with 26 blacks in a row. Observational studies – using casino security footage – have confirmed that it continues to influence bets today.

Surprisingly, education and intelligence do not protect us against the bias. Indeed, one study by Chinese and American researchers found that people with higher IQs are actually more susceptible to the gambler’s fallacy than people who score less well on standardised tests. It could be that the more intelligent people overthink the patterns and believe that they are smart enough to predict what comes next.

There’s more at the link.

I’ve seen this error at work in many ways, and made it myself on more than one occasion.  It falls under the heading of “probability errors”, of which there are more than a few.  (There’s an interesting discussion of that topic here:  I recommend clicking over there to read it, to learn from others’ mistakes before we make them ourselves.)



  1. One of the things tabletop role playing games will teach you (by direct exposure) is a bit about probability.

    Now, it can get wildly complex with some systems (dice pools, for example), but for others it's straightforward. A twenty-sided die, for example, even if you roll it ten or twenty or a hundred times, your chances of getting a specific result are still: 1 in 20.

    It can be absolutely infuriating and sanity-eroding to be on the wrong end of a run of luck. And as much as my engineer friend lectures me on 'random chunks of plastic', sometimes the dice are so cruel you wonder what's going on.

  2. In the coin flipping analogy, and in may courses, a coin flip is described as a binary choice. It isn't. In a very small percentage of cases, the coin will land on it's edge. While this doesn't change the thrust of the story, it should be kept in mind.

    The chance of being killed by a meteor coming thru your roof is very small, but not zero.

  3. When quoting such statistics the presenter will always state "assuming a fair die, coin, or whatever mechanism under discussion."
    A long string of one result introduces the question of some outside force manipulating the fairness which for any physical object is not perfect. You can have loaded dice, a two headed or tailed coin, or a host of schemes developed to cheat the rules of chance.
    Interestingly, most jurisdictions do not consider poker a game of chance, and rightly so. A competent player depends two thirds on skill and the remainder on the luck of the draw. And that skill consists of both knowing the percentages of winning any particular hand and the ability to read one's opponent. Which is why most players consider on line poker a whole different game.

  4. I have been unable to (completely) dissuade my wife of almost 47 years of the gamblers fallacy regarding slot machines. Like most slots players, she still somewhat believes that, if a particular machine hasn't hit in a long time, "it's due."

  5. I worked the roulette wheel in a casino for a while. They told us that putting up the electronic board with the past 10 or so spins increased their profits by over 30% on any given roulette table because of the gambler's fallacy.

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