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The Gambler's Fallacy

On October 18 1913 in the Monte Carlo Casino during a game of roulette, the ball fell in black 26 times in a row. Assuming that the ball couldn’t possibly continue to fall in the black, the gamblers placed bets on red, time and time again. Not only did the gamblers lose on the streak of black, but they lost millions of francs by continuing to bet on red after the black streak had ended in the belief that the imbalance would correct itself with a long streak of red. For the record, the probability of a streak of one colour to come up 26 times in a row is 1 in 66.6 million. This is the most famous example of the ‘gambler’s fallacy’.

The problem with this thinking is the false notion that a sequence of past outcomes shapes the probability of future outcomes. The roulette wheel has no memory, therefore the chances of the ball landing on red or black does not change. This is the difference between probability versus chance.

The easiest way to illustrate the difference between probability and chance is to look at the toss of a coin. The chance of a coin coming up heads or tails is 50% and this never changes. This is because chance is defined as the ratio of chances for one outcome against the chances of another – Tails, one chance. Heads, one chance.

However, probability is defined as the chances for an event divided by the total number of chances. So on the first coin toss, the chance of tails is 1/2. The probability of getting tails twice in a row is one in four (1/2 x 1/2). The probability of five successive tails would be 1/32. So after the fourth successive tails, wouldn’t it make sense to bet heads if the probability of a fifth successive tail is 1/32 (only 3.125%)?

No. Therein lies the fallacy. There is a false reasoning that the next outcome can in some way be influenced by past results. The chance that the coin will come down heads or tails is still 50/50.

The gamblers fallacy has a corollary – the ‘hot hand’. The academic name is ‘positive recency’. There is evidence that those guided by the notion that something that has kept on happening will not reoccur, are equally persuaded by the notion that something that has repeatedly occurred, will carry on happening.

Essentially, these are the fallacies that drive bad investments and stock market strategies. The market is bound to turn or it is bound to crash because it has been high way too long. Decisions need to be based on fact or mathematics and you need to ask yourself; what controls the outcome and am I making this decision based on facts or on a fallacy?

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