Gambler’s Fallacy and How it May Affect You

What is the Gambler’s Fallacy?

If you are thinking about betting or trading long term, you’ll want to know about this. The gambler’s fallacy is a cognitive bias that occurs when a person believes that previous events in a game of chance will influence future outcomes. In other words, a person believes that if a particular outcome has not occurred in a while, it is more likely to occur soon. This is also known as the ‘law of averages’ or the ‘Monte Carlo fallacy.’

Coin Flip Exercise

Let’s say you are flipping a coin. The probability of getting heads or tails is 50/50. If you flip the coin five times and get heads every time, you might start to believe that tails is ‘due’ and is more likely to occur. However, in reality, the probability of getting heads or tails is still 50/50, regardless of what has happened in previous coin flips. A coin has no memory, and each time it is tossed, the probability of heads or tails remains the same at 50% or odds of 2.0 . The gambler’s problem is that he thinks the fairness of the coin gives him reason to expect that any change in one direction will soon be cancelled out by a corresponding change in the other.

Monte Carlo Fallacy

One of the most well known examples of the gambler’s fallacy, occurred at the famous Monte Carlo casino in 1913. At the time, the Roulette wheel had landed on black twenty-six times in a row. During this run of black, many people believed that red was bound to land ‘soon’ and started placing large bets on it. However, the ball landed on black again and again, causing many people to lose significant amounts of money. This event became known as the ‘Monte Carlo fallacy’. The roulette players believed, incorrectly, that the odds of another black number landing were becoming ridiculously high, highlighting their irrational belief that one spin somehow influenced the next.

The Impact of Gambler’s Fallacy on Bettors

It stands to reason that The gambler’s fallacy can have a significant impact on gambling behavior. For example, if a person believes that a particular outcome is ‘due’ and places a large bet on it, they may end up losing a lot of money. This is because the outcome is still subject to chance, and previous outcomes have no bearing on future ones.

Cognitive Bias and Psychological Heuristics

The gambler’s fallacy is just one example of cognitive bias and psychological heuristics. Another example is the representativeness heuristic, where a person makes a judgment based on how closely something resembles a ‘typical example’. This can impact gambling behavior, as a person may believe that a particular outcome is more likely because it fits their idea of what a ‘typical’ outcome should be.

Can you Overcome the Gambler’s fallacy?

This can be challenging but not impossible. Here are some tips:

1. Understand Probability: The Gambler’s fallacy is based on the misconception that the probability of an event changes based on previous outcomes. However, the truth is that each event in a game of chance is independent and has the same probability of occurring as any other event. Educating yourself on probability and how it works can help you overcome this cognitive bias.
   
2. Use a Betting Strategy: Using a betting strategy can help you avoid making impulsive bets based on the Gambler’s fallacy. For example, you could set a limit on the amount of money you are willing to spend on each bet or decide on a fixed number of bets before stopping.
   
3. Focus on the Present: To overcome the Gambler’s fallacy, it’s important to focus on the present and not the past. Instead of thinking about previous outcomes, concentrate on the current event and its probability of occurring.
   
4. Take Breaks: Taking breaks during a gambling session can help you reset and refocus. Stepping away from the game can help you avoid becoming emotionally attached to previous outcomes and reduce the impact of the Gambler’s fallacy.
   
5. Seek Professional Help: If you find that the Gambler’s fallacy is impacting your gambling behavior, seeking professional help can be beneficial. A therapist or counselor can provide support and guidance to help you overcome this cognitive bias.
   

The Law of Small Numbers

The law of small numbers refers to the idea that a small sample size of data can sometimes provide misleading information or results.

What is the Law of Small Numbers?

The law of small numbers is a statistical concept that suggests that a small sample size may not be representative of the entire population. In other words, if we draw a conclusion based on a small sample size, the result may not be accurate or reliable. The law of small numbers can affect many areas of life, including science, economics, and betting and gambling.

The Law of Small Numbers and Betting and Gambling

In the context of betting and gambling, the law of small numbers means that a small sample size of bets or trades may not accurately represent the long-term outcome.

Examples of the Law of Small Numbers in Betting and Gambling

1. A bettor places five bets on a sports team to win and loses all five bets. The bettor may assume that the team is not good and avoid betting on them in the future. However, the sample size of five bets is too small to make a conclusion about the team’s overall performance.
   
2. A gambler plays a slot machine and wins two jackpots in a row. The gambler may assume that the machine is ‘hot’ and continue playing, but the law of small numbers suggests that the two jackpots are not indicative of the machine’s long-term payout rate.
   
3. A bettor places a bet on a horse race and wins three times in a row. The bettor may assume that they have a ‘system’ for picking winners and continue betting, but the law of small numbers suggests that the three wins are not enough to prove the validity of the system.

The gamblers fallacy is related to the law of small numbers because it often occurs when a small sample size is used to draw a conclusion.

Sports bettors are particularly vulnerable to pattern recognition where the ‘pattern’ is either not really a pattern and / or will not exist over the long term.

Look at the sports betting graph below and the hypothetical profitability of 100 bets. Each bet is placed at a price of 2.0 (even money). Doesn’t it looks like a really profitable strategy?

It’s the next graph of 1000 bets that shows us the true picture:

The strategy is not if fact profitable at all, at least not over the duration of 1000 bets. This doesn’t mean that the strategy couldn’t recover and go on to be profitable, however, it is not very likely.

Look at these 1000 bet charts below:

The data for these graphs were created by a random number generator. Notice the large range of variance between the graphs. Now check out the graph in the centre, which is showing a decent profit over 1000 bets, but the profit shown is pure chance.

How long will it take you to reach 1000 bets with your betting style? A year? five years? Maybe ten years? Many people never find out if they are actually profitable, or just being lucky.

The table below shows the probability of still being in profit after a specific number of bets, with a negative expectation of -2.5%.

You can see from the table, that after 1000 bets there is still around a 20% chance of being profitable or ‘lucky’, even though it is a losing strategy. That is odds of 4/1 or 5.0 decimal, which land quite often, so you need to be careful.

The Law of Large Numbers

The Law of Large Numbers was first discovered by Jacob Bernoulli in the 17th century, which demonstrates that the more extensive the sample size of an event, the more likely it is to represent its true probability. For instance, a fair coin toss has an equal 50% chance of hitting heads or tails. Bernoulli calculated that as the number of coin tosses gets larger, the percentage of heads or tails results gets closer to 50%. However, the difference between the actual number of heads or tails thrown gets larger.

Gamblers and bettors have always struggled to comprehend Bernoulli’s theorem.

Bernoulli’s discovery shows that as the sample of coin-tosses grows, the distribution of heads or tails will correct to around 50%.

With such a large sample. however, the expected deviation from an equal 50/50 split can be vey big in the ‘many hundreds’. Going back to the Monte Carlo fallacy, you can understand how the mistaken belief that runs of red or black will even out over a short period of play, can be very destructive to gamblers.

Slot Machines

Another classic example relates to slot machines, which are basically random number generators, with Return to Player (RTP) settings. You see it all the time, slots players pumping coins into a machine without success and often ‘hogging’ it, believing that a big win must follow their losing run. This isn’t a tactic that’s viable. The player would have to have played an inordinately large number of times to hit RTP.

Tying It Up

The gambler’s fallacy is a cognitive bias that can impact gambling behavior. It occurs when a person believes that previous events in a game of chance will influence future outcomes. By understanding this fallacy and other related cognitive biases, individuals can make more informed decisions when it comes to gambling. Remember, each outcome is still subject to chance, regardless of what has happened in the past.

Below you can read more about general fallacies.

What is a Fallacy?

A fallacy is a mistaken belief or reasoning that leads to incorrect conclusions. There are many types of fallacies, and they can occur in various fields, including logic, argumentation, and decision-making.

There are many types of fallacy but five well known ones are as follows:

1. The Red Herring Fallacy – This fallacy occurs when someone introduces an irrelevant topic to divert attention from the main issue.
   
2. Strawman Fallacy – This fallacy occurs when someone misrepresents or exaggerates an opponent’s argument to make it easier to attack.
   
3. Slippery Slope Fallacy – This fallacy occurs when someone argues that a small event will inevitably lead to a much larger, undesirable event.
   
4. Begging the Question Fallacy – This fallacy occurs when someone assumes that their conclusion is correct without supporting it.
   
5. Post Hoc Fallacy – occurs when one assumes that because one event follows another, the first event caused the second event.

The Red Herring fallacy

The Red Herring Fallacy is a tactic used to distract or divert attention from the topic at hand by introducing irrelevant information or arguments. This fallacy is often used in debates or arguments to derail the conversation and confuse or mislead the audience.

For example, if two politicians are debating a proposed tax reform, one might introduce an unrelated topic, such as national security, to shift the focus away from the tax reform. This is a Red Herring Fallacy because the introduced topic is not relevant to the original argument.

Another example of the Red Herring Fallacy is when someone attacks the person making the argument instead of addressing the argument itself. For instance, if someone argues that climate change is a serious issue, and their opponent responds by attacking their personal character, this is a Red Herring Fallacy.

It’s important to be aware of the Red Herring Fallacy when engaging in debates or discussions. When someone introduces an unrelated argument or attacks the person making the argument, it’s important to redirect the conversation back to the original topic.

Straw Man Fallacy

The Strawman Fallacy (also known as ‘strawman’) is a type of argumentative fallacy where one misrepresents or distorts their opponent’s argument in order to make it easier to attack or refute. The name ‘straw man’ comes from the idea of creating a fake opponent made of straw that is easy to knock down.

This fallacy is often used in political debates and discussions where one side wants to discredit their opponent’s argument without actually addressing it. For example, if someone argues for stricter gun control laws, their opponent may misrepresent their argument by saying they want to take away all guns, which is an extreme and inaccurate representation of the original argument. By attacking this distorted argument, the opponent is able to avoid addressing the actual argument for stricter gun control laws.

Another example of the Strawman Fallacy is when someone argues against a weaker version of their opponent’s argument instead of the actual argument. This is done in order to make it easier to refute the argument. For instance, if someone argues that we should have stricter laws against hate speech, their opponent may misrepresent their argument by saying they want to abolish free speech altogether. This is a weaker and inaccurate representation of the original argument, making it easier to refute.

To avoid using the Strawman Fallacy, it’s important to accurately represent and understand your opponent’s argument before responding to it. Instead of misrepresenting or distorting their argument, address the actual argument to engage in productive and respectful debate.

Slippery Slope Fallacy

The Slippery Slope Fallacy is a type of argumentative fallacy where one argues that a certain event or action will lead to a chain reaction of increasingly negative events, without providing any evidence to support this claim. This fallacy is often used to discourage taking action by painting a bleak future that is not necessarily based on reality.

For example, in the context of politics, someone might argue against implementing a compulsory vaccine program, which will then lead to a complete loss of personal choices. This argument fails to provide any evidence to support the claim that implementing the program will inevitably lead to a loss of personal choice or freedoms. The vaccine program can of course be implemented as a ‘one off’ without affecting people’s rights and choices regarding other matters.

Another example of the Slippery Slope Fallacy can be found in personal relationships. Someone might argue against introducing their significant other to their family by saying that it will lead to their family disliking their significant other, which will then lead to a break-up. This argument fails to provide any evidence to support the claim that introducing their significant other to their family will inevitably lead to a break-up. It also fails to acknowledge that there are many factors that contribute to the success or failure of a relationship, and that meeting one’s family is not necessarily a make-or-break situation.

To avoid using the Slippery Slope Fallacy, it’s important to provide evidence to support any claims about the future. Instead of assuming that one event will inevitably lead to a chain reaction of negative events, acknowledge that there are many factors that can influence the outcome of a situation.

Begging the Question Fallacy

The Begging the Question Fallacy, also known as circular reasoning, is a type of argumentative fallacy where the conclusion of an argument is assumed in the premise. In other words, the argument is based on an assumption that has not been proven, and the conclusion is then used to support the same assumption.

For example, someone might argue that ghosts are real because they have seen them, and since ghosts are real, their sightings must be real as well. This argument begs the question by assuming that ghosts are real without providing any evidence to support this claim.

Another example of the Begging the Question Fallacy can be found in debates about religion. Someone might argue that the Bible is true because it is the word of God, and since the Bible is the word of God, it must be true. This argument begs the question by assuming that the Bible is the word of God without providing any evidence to support this claim.

To avoid using the Begging the Question Fallacy, it’s important to provide evidence to support any assumptions that are made in an argument. Instead of assuming that a certain premise is true, provide evidence to support it and make sure that the conclusion is not based solely on the assumption.

Post Hoc Fallacy

The post hoc fallacy, also known as the ‘false cause fallacy,’ occurs when one assumes that because one event follows another, the first event caused the second event. Yet, just because two things happen in sequence, it doesn’t necessarily mean that one caused the other.

For example, if someone wears a lucky shirt and then wins a game, they might assume that the shirt caused their victory. This is a post hoc fallacy because there is no direct evidence to support the idea that the shirt had any influence over the outcome.

The post hoc fallacy is commonly used in advertising, where companies may suggest that their product caused a positive outcome, even if there is no direct evidence to support the claim. For example, a shampoo company might imply that their product caused someone’s hair to grow faster or become thicker, even though there is no scientific evidence to prove it.

It’s important to be aware of the post hoc fallacy, as it can lead to false beliefs and misguided actions. When evaluating cause-and-effect relationships, it’s important to look for direct evidence of causation, rather than simply assuming that two events are related because they occurred in sequence.

Conclusion

There are many types of fallacy, over a hundred, generally split into ‘formal’ and ‘informal’ categories. You can find more information here.