The FloodFlash behavioural science series: The Gambler’s Fallacy

Last month, we explored herd behaviour. This is when individuals follow others and imitate group behaviours rather than making decisions independently. Check out the full article here. This month, we’re covering the gambler’s fallacy. We’ll explore what it is and what it means for flooding and flood insurance.

What is the gambler’s fallacy?

The gambler’s fallacy assumes that a random event is more or less likely depending on the outcome of a previous event or a series of events. Take a coin landing on heads three times in a row. The tendency is to think ‘the fourth toss must be tails.’ The same applies to a dice roll or entering the lottery. 

Casinos are a common site for the gambler's fallacy.
Slot machines are a great example of where the gambler’s fallacy plays a key role. Many players will assume that they are ‘due’ a win after a string of losses, despite every turn having a random outcome.

The fallacy was first described over two centuries ago. French polymath Maquis de Laplace noticed that men often thought that the more boys who were born, the more likely their own child would be a girl. An experiment in the 1960s showed the gambler’s fallacy for the first time in experimental settings. Two coloured lights were illuminated in random patterns. When one colour lit up multiple times in a row, subjects commonly guessed that the other light would illuminate next. 

We typically use the outcome of past events to decide on a future event. When we see grey clouds in the sky, we decide to take a raincoat or an umbrella with us. Past experience has told us that grey clouds are good indicators of rain – they are causally related.

The problem arises when two events are not causally related – one does not have an impact on the other – but we think that they are. We then base a decision surrounding a future event on the wrong information. Like many of the behavioural science phenomena in this series, falling victim to the gambler’s fallacy can lead to sub-optimal decision making. 

Why does it happen?

Events like a dice roll or a coin toss are independent. This means that the outcome of previous events has no bearing on future events. Independent events are random, and, as a rule, humans don’t like randomness. Despite what some people may think, most of us like predictability, order, and certainty in most areas of our lives. One reason why many of us fall victim to the gambler’s fallacy is due to this human instinct to turn random events from unpredictable to predictable.

The ‘law of small numbers’ also plays a role in the gambler’s fallacy. This law describes the action of taking small samples of information to represent the larger population. This behaviour is related to the availability bias, where we use information that comes to mind quickly and easily when making decisions. See here for our full explanation of availability bias.

The gambler’s fallacy in action

Casino games are the most common example of the gambler’s fallacy in action. The most famous example involves the roulette tables of a Monte Carlo casino over 100 years ago. The roulette wheel landed on black 10 spins in a row. Players started betting against black, under the impression that a red was long overdue. However, the (random) trend continued, and it was only after 26 consecutive blacks that the ball finally landed on red.

The fallacy has wider implications too, including in the financial world. Economists Hersh Shefrin and Meir Statman suggest that investors have a ‘general disposition to sell winners too early and hold losers too long’. If a stock falls in price, investors think ‘it can’t keep falling forever, so I’ll hold onto it until it rises again’. If a stock rises in price, investors think the opposite. Often, these decisions are based on the history of the stock price, despite this not necessarily being related. 

Investors have a general disposition to sell winners too early and hold losers too long - largely due to the gambler's fallacy.
The gambler’s fallacy can be seen in investing patterns, with investors typically holding onto falling stocks too long and selling rising stock too early.

What does gambler’s fallacy mean for those at risk flooding?

Many of those at risk of flooding fall victim to the gambler’s fallacy. They experience a flood, and subsequently believe there will not be another for several years. Flood risk is often defined in a way that encourages this belief. Most commonly, flood risk will be described in the format of a ‘1-in-number of years’ event. For example, a ‘1-in-100-year’ event. Individuals often incorrectly asume that this means a flood will happen every 100 years.

However, a 1-in-100-year event means that modelling suggest a flood would happen 1 time in 100 years. Thinking back to our die or coin examples, we know that statistical probability rarely predicts reality. The probability of a die landing on a 6 is one time in six. But a die can land on a 6 more than once after six rolls. It can also not land on a 6 for more than six rolls. Likewise, a coin doesn’t alternate perfectly between head and tails. Of course, if you were to roll a die or toss a coin a million times, the number of sixes would be close to a sixth of the rolls, and the number of heads close to a half of the tosses. The same is true for flooding. The chance of flooding may be 1-in-100. But the chance remains the same every year whether you’ve flooded or not.

One of our own claimants had significant flooding in both 2015 and 2022, despite being in a 1-in-100 year flood zone.

‘[After the 2015 flood] we put some plans in place and thought this would never happen again. They said it was once in 100 years. This weekend, this has happened – we’ve flooded.’

Sarah, Practice Manager at Tadcaster Medical Centre, after flooding during Storm Franklin in 2022
Tadcaster Medical Centre suffered catastrophic flooding in 2015 and 2022, despite being in a 1-in-100-year flood zone.

What does the gambler’s fallacy mean for flood insurance?

The eagle-eyed readers amongst you may be thinking back to our blog on availability bias. The availability bias suggests that after a flood, people will be more likely to get insurance. The gambler’s fallacy suggests the opposite, that after a flood, people will be less likely to get insurance. Ultimately, which behavioural science phenomenon reigns depends on multiple factors. Research into the demand for typhoon insurance in China found that two key factors were the gender of the decision-maker, and the number of typhoons experienced. Females are more likely to be susceptible to the availability bias, while males will tend to follow the gambler’s fallacy. Those who experience multiple typhoons are more strongly influenced by the gambler’s fallacy.

The scale of previous flooding is also important, according to researchers in the U.S. When policy-holders experience a small flood, they are more likely to hold onto their policy for longer. When they experience a larger flood, they tend to let their insurance lapse earlier. They believe they’ve had all their bad luck and won’t be ‘due’ another flood in their near future.

The gambler’s fallacy often results in people under-preparing for a flood event when they have recently experienced one. As a broker, it’s important to remind your client that their risk of flooding is exactly the same the year after they flooded. Floods don’t happen at regular intervals, and it is almost impossible to predict when a flood will occur outside of a few days prior. Climate change is also making it harder to accurately reflect the chance of a flood event, meaning the flood zone your client is in may be outdated. For collateral to help support conversations with your client, get in touch at