In 1913 the world famous Monte Carlo Casino in picturesque Monaco witnessed one of the most famous events in gambling history. Almost unbelievably, especially for those in attendance, black fell an amazing 26 times in a row. As stunned players looked on the ball continued to fall into a black number spin after spin. And with one black number after another, players bet more on red thinking that probability was increasing in their favour. Red just had to come up, the more blacks that were spun, the more likely it was that the little white ball would drop onto a red number. But was that really the case? With each black that landed, did the probability of the next spin being a red increase?
Well no, actually not at all. Each individual spin of the roulette wheel is an independent event with no relation to the spin preceding it. While being an uncommon occurrence, 26 black numbers in a row is no different to the other 67,108,863 combinations of red and black that can be seen in 26 spins of the roulette wheel. So why did the players at the casino think that with each black number the chances of a red number increased? Why do players even today look at the number boards when placing bets on the roulette wheel? The answer unfortunately for most is simply psychology. In fact the phenomenon is so common it has become known as the “gambler’s fallacy“.
In short, the gambler’s fallacy is the mistaken belief that if an event occurs more frequently than normal during a period of time, it is less likely to occur in the future (and vice versa). In situations where each event is truly random such as the spinning of the roulette wheel or the flipping of a coin, this presumption is false. And while gambler’s fallacy is mostly associated with gambling, it can also be seen in other areas of life such as childbirth where people mistakenly believe that having one or more children of one gender increases the likelihood of having the opposite gender with the next born child.
The gambler’s fallacy arises from the mistaken belief that small samples represent a larger population, and that any departure from what occurs on average must be corrected in the short term.
Lets use the classic example of a coin toss. Using a fair coin with no bias, on each toss there is a 50% chance of the coin coming up heads, and a 50% chance of the coin coming up tails. So for our first toss you are asked to guess which will land, what would you choose? Now what if heads landed 10 times in a row and you are again asked to guess which way the coin would land, would you be inclined to select tails?
The probability of tails being tossed is still 50%, no different to the very first toss. In fact the probability of there being 11 heads tossed in a row and 10 heads and 1 tail are exactly the same. While over a large enough sample we would expect to see heads and tails evenly distributed, it is dangerous to make assumptions based on smaller sample sizes.
So why is it important for us to know about the gambler’s fallacy when betting on sport? Well results and the studying of previous form can sometimes falsely lead us to betting on an outcome.
Let’s again use the example of the Australian Tiddlywinks League. Since its inception, 55% of home teams win their matches, but on one weekend 4 out of 4 matches are won by the away team. In the last game of the weekend the Brisbane Bandits are at home against the Perth Pumas. Would we expect that because no other home team has won the Bandits will win?
Of course there simply isn’t enough information to make a good judgement, and the Bandits and Puma’s match is a completely independent event from the other 4 matches played. If we looks more deeply into the match we would see that the Bandits were $3.00 outsiders and were missing their superstar player. And that in this particular weekend the bottom 5 teams on the ladder also happened to be hosting the top 5 teams. On top of that at the half way point of the season 65% of home teams had won their matches.
Similarly when developing a handicapping model it is important to gather a significant sample so as to avoid sampling errors. In fact some handicappers use decades worth of data when developing models for this very reason, the larger the sample size the more likely it will be a true representation of the probability of an event occurring in the future.
So just remember next time you’re at the casino and you just know red is due to come up because of a previous run of black, or that a home team must win a match this weekend, remember those people back in 1913 at the Monte Carlo Casino and the gambler’s fallacy. You might just save yourself from an easily avoided loss.