On the 18th of August 1913, there was a stir in the Casino de Monte Carlo
in Monaco. A crowd had gathered around the roulette table.
Each time, as the wheel slowed to a stop, you could hear more and more audible gasps from the
onlookers. In the end, the ball landed on black 26 times in a row. But as the streak had gone on,
millions of francs were lost as gamblers became convinced that it would end on the next roll.
This belief - the belief that unusual trends in completely independent events must somehow
even out over time - has been given a name by mathematicians: the gambler’s fallacy.
A ‘fallacy’ is a name given to a mistaken belief that is based on
unsound reasoning. Let’s have a think about why those gamblers in Monte Carlo
were wrong to think their chances of winning became higher as the black streak continued.
A roulette wheel has thirty-seven segments where the ball can land: 18 are red, 18 are black,
and one is green. Assuming the wheel is “fair,” when you spin the wheel and drop the ball in,
there is a 1 in 37 chance of the ball landing on any one of the segments on the wheel.
Importantly, though, spinning a roulette wheel is an independent event of chance.
Regardless of what has happened before or what will happen after, the odds of a ball landing
on any segment of a fair roulette wheel do not change; they will remain 1 in 37 no matter what.
The people in that casino in Monte Carlo were struggling to believe
that complete randomness could exist in the world.
They mistakenly thought that the black streak that they were experiencing meant that the
chances of rolling a red must have been higher than the 18 in 37 that they actually were.
The gambling fallacy also exists as a phenomenon in football. There are plenty
of examples of footballers talking about things that happen on the football field
using something equivalent to gambler’s fallacy as justification. Former England,
Leicester City and Tottenham striker Gary Lineker chose not to shoot during pre-match warm ups,
claiming he didn’t want to "waste" goals and use up his “good stuff” before the game.
Harry Kane has also used gambler’s fallacy-like logic when talking
about his thought processes during matches. Speaking to The Telegraph in 2015, he said,
“(Jermain) Defoe told me once ‘if I miss a chance then the odds are now in my favour
to score the next one because the chances of missing two in a row are less than missing one’.
And that’s what I try and take (shots). If I miss, then the next one is more in my favour to score.”
It’s worth noting at this point that when it comes to footballers shooting, these aren’t
technically examples of the gambler’s fallacy. As we saw in the case of the Monte Carlo example,
the gambler’s fallacy only applies in instances where the events being considered are causally
unrelated to one another. When it comes to Harry Kane shooting, the odds of him scoring will
change every time based on a myriad of factors including the outcome of the previous shot.
Where he is wrong is in stating categorically that the odds of
scoring the next chance will always rise if he misses a shot. This is simply not true.
Perhaps a purer example of the gambler’s fallacy emerges during penalty shoot-outs.
In an academic study carried out by researchers from University College London,
they looked at keepers' dive patterns in all 37 penalty shootouts in World Cup and European
Cup matches between 1976 and 2012. They noticed that, after a ball had been aimed to one side,
keepers were more likely to dive the other way for the next shot, and the odds increased if a
second or third ball had gone to the same side. For example, after three balls had been directed
to one side, goalkeepers directed more than 70% of their dives for the fourth ball the opposite way.
Again, penalty kicks in a shoot-out are not completely causally unrelated,
but goalkeepers here are clearly using gambler’s fallacy logic to influence
their decisions to dive in a different direction in the course of the proceedings.
What is perhaps most interesting here is the psychological element.
In the case of the striker shooting or the goalkeeper diving, the logical
explanations given for these decisions are less interesting than the outcomes they produce.
For Harry Kane, whether the gambler’s fallacy is a fallacy or not is unimportant, what matters is
that it gives him a foundation for believing that his next shot is more likely to result in a goal
if he missed the last one. In these instances, the logic - or lack of logic - is immaterial.
What matters is that it gives him the psychological edge when lining up his next shot.