The Gambler's Fallacy: Relating it to Your STEM Classes

Teaching STEM subjects comes with many caveats. Not only are the topics often complex (and fascinating!), they demand a way of thinking and analyzing that students may not be accustomed to. In fact, students will probably enter your classroom with some cognitive processes that may make STEM subjects difficult.

One of those is the gambler’s fallacy – where a person incorrectly thinks that a random event in the future is/can be shaped by the frequency of events in the past. In other words, if an outcome happens multiple times, the opposite outcome will be more likely moving forward.

But what does the gambler’s fallacy have to do with STEM? And how can you help students alleviate their gambler’s fallacy tendencies? We explain below.

What is Gambler’s Fallacy?

The gambler’s fallacy is a term commonly used when someone is betting. It’s also known as the ‘Monte Carlo fallacy’ and refers to when a person believes that an outcome is more or less likely to happen based on the outcomes they’ve previously seen. For example, when rolling dice, the person betting may mistakenly think that they’re more likely to get a six because the dice rolls beforehand didn’t produce a six.

The gambler’s fallacy is a cognitive bias called the ‘representative heuristic’ in psychology. Heuristics are mental shortcuts that human brains use to make decisions quickly. The gambler’s fallacy can also be applied to scenarios outside of gambling, whereby a person has conviction that past events will influence future ones, even if those events are completely separate from one another.

Gambler’s Fallacy Examples

The most famous example of the gambler’s fallacy is the event from which it got its name. In 1913, a game of roulette in a Monte Carlo casino saw the ball land on black 26 times in a row. Gamblers in the casino began placing huge bets on red, as they believed the frequency of the past black lands couldn’t be repeated. A lot of people lost a lot of money due to the gambler’s fallacy.

Another example is guessing the sex of a baby. Parents may be inclined to think that if they’ve had three boys, their fourth child will be a girl. Despite knowing that the sex of a baby is not determined by the frequency of boys/girls they’ve had before, people still suspect that there is a relationship between the two likelihoods.

The gambler’s fallacy could additionally show up at a spelling bee. If a contestant didn’t get as far as they wanted in previous years, they may think that this time around, there’s a higher chance of them being successful. However, their performance in previous contests has no bearing on their performance in the upcoming one.

How to Avoid the Gambler’s Fallacy: STEM Classroom Edition

We may all invoke the gambler’s fallacy at some point in our lives, but it can be dangerous in STEM subjects, where students have to think with a causal mindset. Causality is about being able to prove a direct cause and effect – not a feeling, assumption or perceived outcome based on random actions – and it relies on clear facts and data.

If a STEM student moves forward with the gambler's fallacy, they risk making incorrect calculations and conclusions. Students should determine outcomes based on empirical probability, not the guesswork that comes with the gambler’s fallacy. By educating students early on in their STEM journeys, they will understand and avoid the gambler’s fallacy trap, which in turn will keep calculations accurate and representative.

As the teacher, it’s important to highlight how and when the gambler’s fallacy is playing a role in students’ thinking, and explain why this line of thinking is flawed. You should be able to demonstrate why the events are independent of one another, and break down why the student may think that a past event influences a future one.

Interestingly, studies have found that honing in on the definition of probability and randomness isn’t always effective to reduce gambler’s fallacy. A good way to present this fallacy to your students is to treat each outcome of a random series like it’s the very start of that series, not an extension of it. By making this distinction, students will be less inclined to make connections to earlier results.

The gambler’s fallacy is just that – a fallacy, mistaken reasoning. Students in STEM have to quickly adapt to thinking logically, and being able to rationalize their approach with sound data and practices. Guided by teachers, students that can recognize the gambler’s fallacy in their own reasoning will see progress in their STEM courses.