The Gambler’s fallacy: Not just for gamblers

gamblers fallacy

Seated confidently at a betting table, a gambler experiencing a “hot hand” can feel the rush of adrenaline that accompanies a winning streak. Said gambler bets again, but worries that he’s due for a loss since his wins on this 50/50 game of chance have been so numerous. To his surprise, he wins again.

Consider the same scenario, but now, the player’s attitude is different. Unlike our other friend, this gambler plunks down all of his winnings, confident that because he’s on such a roll, his lucky streak will continue and to his surprise, he loses it all.

In both scenarios we witness different ways in which the Gambler’s fallacy (also known as the Monte Carlo fallacy) can play out. To put the Gambler’s fallacy into perspective, let’s look at a coin flip. While this is probably the most used example to illustrate probability in mathematics, it explains the fallacy very effectively. When flipping a coin, there is a 50/50 chance that on any given turn you will either get heads or tails. Just because you get tails five times in a row, does not mean the probability of getting tails on your next try becomes higher than 50%. Similarly, in the two scenarios above the probability of an event occurring is 50/50.

The problem with this line of thinking? Past events do not change the probability that certain events will or will not occur in the future.  So next time you flip a coin and it lands on tails 15 ties in a row, don’t assume that “The next flip will probably be tails.”

Although it may not seem like it, the reality is that the odds for each and every flip are calculated independently from other flips. The chance for each flip is 50/50, no matter how many times heads came up before. Each event occurs independently from the previous event; the coin has no thoughts, nor does the universe seek to establish some sort of balance on account of the overwhelming number of “heads” flips. Each flip is an independent event.

In hindsight, it’s easy to witness the Gambler’s fallacy in the scenarios described above. Yet, it occurs daily in nearly everyone’s life, whether they gamble or not. How many people know a family of three boys with a fourth child on the way and think to themselves, “well, it’s bound to be a girl – they’re due for one!” What about the frequent lottery player who has bought a ticket religiously every Monday for 10 years, and who just knows his next ticket will be a winner because the universe somehow owes him a win after so many losses?

Anyone who has stepped foot in a casino is probably guilty of committing the Gambler’s fallacy. Its proliferation across countless circumstances, gambling-related or not, though, is what many fail to recognize. Humans, because of our ability to experience emotions, create patterns and assign value to items that otherwise do not have value in a logic-only world, and thus fall into the trap of the Gambler’s fallacy often.

In their article “Sympathetic magic and perceptions of randomness: The hot hand versus the gambler’s fallacy”, doctors Lana M. Trick and Christopher J. R. wrote that the Gambler’s fallacy happens because of a natural tendency for people to organize separate events into larger units, grouping events that form episodes or meaningful patterns rather than seeing each event separately. Additionally, similarly to the Gambler’s fallacy, they observed another interesting tendency individuals have known as the hot hand. This can be seen as a variation of the Gambler’s fallacy as it occurs when individuals expect a run of events whose outcomes occur by pure chance to continue occurring in the same way.

This isn’t to say that past events never influence future occurrences; on the contrary, in some cases certain events can greatly influence the probability of an event happening. For example, if you played a game of trying to guess what color marble you will pull out of a bag filled with 100 marbles, half of them red the other half blue, you start out with a 50/50 chance of pulling either a blue or a red marble. Like in the case of the Gambler’s fallacy, it would be inaccurate to assume that what you pull out of the bag the first time is anything but a product of chance. Unlike the fallacy, however, as you pull red or blue marbles and set them aside, the probability of getting either color changes. In this case it would be reasonable to assume that since you have already pulled seven blue marbles, there is a higher probability of pulling a red one, since there are more red marbles in the bag. This isn’t the same as the Gambler’s fallacy and should not be confused because in casino games such as roulette, the probability never changes, no matter how many rolls.  This bias isn’t limited to gamblers. Otherwise bright, logical people can be caught in the trap of the Gambler’s fallacy. They will inevitably make the mistake of assuming that the universe “owes” them something, or that a string of bad luck (or good luck!) must lead to the opposite sometime soon.

Beliefs in karma or universal balance aside, logic prevails when it comes to the Gambler’s fallacy – that is, after all, why it’s called a fallacy. Those of us who have an understanding of statistics will recognize when the Gambler’s fallacy creeps into their thoughts or motivations and can address the situation logically, while experiencing a series of wins or losses. It’s those who recognize the fallacy’s existence in all aspects of life, though, who will be best equipped to handle an unlikely series of events with solid, unencumbered reasoning.