# Why We Play Lotteries, Even If The Numbers Don’t Stack Up – Monash Lens

It is difficult to conclude that human behavior is always rational. Once in a while, we “do things right”, but it is extremely rare to behave in the most rational, logical and utility-maximizing way possible.

We are all invariably victims of an array of cognitive biases that (temporarily) hijack our ability to critically assess a scenario and come up with a thoughtful and logically optimal response.

Let’s say you’re at a carnival and someone offers you a bet that could win you $1,000. The game is simple: you just need to choose a green ball from a barrel containing a bunch of red balls and only a few green balls.

Sounds pretty easy, doesn’t it, and you win $1,000 if you choose a green ball. The problem is that it will cost you $50 to play the game. Do you have to?

Well, to answer that question, you really need to know the probability of winning. In other words, how many red balls are there and how many green balls are there?

First consider the case (we’ll call it ‘Game One’) where there are 90 red balls and only 10 green balls. In other words, out of 10 balls, there are nine red and only one green.

In this example, you have a 1 in 10 chance of choosing a green ball, or rather, a 10% chance of winning. So on average you can expect to earn 10% of the time. Since each time you win you get $1000, your expected return on a single play is 10% of $1000, or $100 (‘chance of winning’ x ‘prize’).

You should also remember here that it will cost you $50 to play. It is clear that your expected return of €100 exceeds your cost of €50, so you should definitely take the bet.

Now imagine a similar game (still costing $50), but this time there are 99 red balls and a single green ball (we’ll call it “game two”). Using the same logic as in Game One, you now have a 1 in 100 (or 1%) chance of winning. Again, your prize is $1000 if you win.

So your expected return on a single play is now 1% of $1,000, or $10. The equation is similar but becomes: $50 (cost) against an expected return of $10. Since your cost ($50) is greater than your expected return ($10), you would not play. It would be irrational.

So play the first game but stay away from the second game.

In a more general sense, the cost of doing something (in this case $50) should be weighed against the outcome you can expect from doing it (in this case, the $1,000 payment multiplied by the probability whether that happens, here either 10% or 1%). When the cost is more than the expected return, don’t. When the cost is less, do it.

The math is relatively simple when the cost, reward, and probability are precisely known, but life decisions are very rarely that precise.

## Playing the lottery is a good example

Most people who play lotteries have at least some kind of intuitive understanding that they are unlikely to hit the jackpot.

Knowing the exact probability of a given outcome seems to be quite important. After all, life is really about probabilities.

Take Powerball in Australia. I will try to be generous and over/understate everything in favor of the bettor.

The cost to play is just over $5. The odds of winning the Premier League are just under one in 130,000,000. On February 24, 2022, the Premier League prize pool is $120 million. So our cost is $5 and our expected return is 120,000,000 * 1/130,000,000 = $0.92. So for every $5 you invest, you can expect to get back around 92 cents.

…Awful…

However, to be fair, there are nine prize divisions in Powerball. Instead of hitting the jackpot, you can get a lesser prize. So now we need to weight each of them by their probability of occurring and sum the values.

I’ll spare you the math, but basically we now have a guess of around $5 (cost) versus an expected return of over $1. It’s clearly much more respectable, but still far from fair.

But wait, I hear you saying, the more games you play, the more profitable it becomes (a MAXI entry of 50 games costs $60). So now the cost of our game goes down to $1.20, but that’s still way more than our expected return of $0.92.

You have probably heard that you are much more likely to die on the way to purchasing your lottery ticket than you are to actually win the lottery (some estimates of the odds of dying in a car accident are as alarming as one in 6700, but even if you’re not driving, there’s always the possibility that you:

- being crushed by a falling vending machine (one in 112 million)
- being attacked by a shark (one in 12 million)
- being stung to death by a bee, hornet or wasp (one in 6.1 million)
- fall to death on a plane (one in 1 million)
- be killed by flesh-eating bacteria (one in 1 million)
- drown in a bathtub (1 in 840,000)
- have to go to the emergency room for a pogo stick injury (one in 115,000).

But all is not gloomy. You are also more likely to:

- give birth to identical quadruplets (one in 15 million)

- become an astronaut (one in 12 million)

- become president of the United States (one in 10 million)
- win an Olympic gold medal (one in 662,000)
- win an Oscar (one in 11,500)
- discover that your child is a genius (one in 250)
- live to 100 (one in 3).

The main thing here is that winning the lottery is very unlikely. So you have to ask yourself, “Why is it so popular?”

If people know that something is very unlikely to happen, and it costs them to see if it will, why would they do it? Well, there are several reasons – many of which are rooted in psychology. In no particular order, here are four of the most common.

## 1. Entertainment

It is important to note that some people intuitively realize that although playing the lotto has little or no economic value, it does have entertainment value. Although you are unlikely to make a net monetary gain, there is something else you can get out of it.

It would be absolutely ridiculous to assume that everyone is equally motivated by financial rewards and nothing else. People go to movies, concerts, and sporting events all the time without any expectation of financial gain.

From a purely economic point of view, this behavior may seem difficult to explain. Fortunately, we know humans are driven by more than money, and all sorts of seemingly “irrational” behavior can be explained away quite easily.

## 2. Near misses

In just about any field, there’s an odd allure of almost winning. The near-miss effect describes a very specific type of failure to achieve a goal. The player who makes the attempt approaches it, but does not reach his objective.

In skill-based games like football or basketball, a near miss gives players useful feedback and a type of implicit encouragement (“You were so close, try again”) that has the effect of giving the player hope to succeed in future trials.

Lottery players who get close (maybe they get three or four numbers right – the odds are usually less than one in 1000) take this as a “sign” that they should keep playing, and they do. often. A paper 2009 discovered that near misses activate the exact same reward systems in the brain as actual successes!

## 3. The numbers are too big

Our brains did not evolve to understand large numbers. Robert Williams, professor of gambling studies at the University of Lethbridge, Alberta, suggests that although humans have developed some appreciation for numbers (we can easily understand the difference between being chased by a lion versus 100 lions, for example), we don’t. really ‘understand’ big numbers.

We deal with amounts like, say, six, 24, and 120 all the time, but throughout history it’s never really mattered to measure 18 million of something, or count 50 million something else.

A one in 200 million chance doesn’t seem that different from a one in 3 million chance, for example. Either way, success is very unlikely. Give someone the choice between a 1 in 3 and a 1 in 200 million chance, however, and the difference is really obvious. It’s certainly not that people can’t type in very large numbers, but they don’t make much sense until we stop and think about them.

## 4. Availability heuristics

Simply put, availability/heuristic bias relates to the idea that people judge the likelihood of something based approximately on how easily examples of that thing come to mind.

Take shark attacks. You can probably think of news reports about when a shark bit a swimmer. One of the reasons for this is that this type of story is sensational and will likely be high profile.

How many times have you seen the headline “No Sharks at the Beach Today”? The thing is, because you can easily recall examples of shark attacks, you might be tempted to conclude that shark attacks are far more common than they actually are. In fact, the odds of being attacked by a shark are approximately one in 12 million.

You hear and read stories about lottery winners all the time. Jackpot winners are always in the news, but battlers who have been playing for 20 years without winning are relegated to the annals of obscurity.

Based on this, it is at least reasonable to think that “jackpotting” cannot be so rare. The net effect is that winning seems possible.

So some lottery bettors crave the thrill of the possibility of winning. Others use it as justification to temporarily fantasize about excessive wealth.

For about the price of a cup of coffee, you can reasonably spend several happy hours imagining “what if?”. The excitement of even having a chance to win can be enough to justify the cost of a ticket or two.

Comments are closed.