Lottery Odds and Cognitive Bias: Why We Keep Playing a Game We Know We'll Lose

Jai Pandey
Jun 27
6 min read

Updated: Jul 11

On November 8, 2022, Edwin Castro walked into a gas station in Altadena, California and walked out with a Powerball ticket worth $2.04 billion. The largest lottery jackpot in history. One ticket with One in 292 million odds.

The next day, millions of people bought tickets anyway.

It's not irrational. It's something more interesting than that. It's the human brain doing exactly what it was built to do, just in a way it was never designed for.

How Absurd the Numbers Really Are

Statistics professor Steven Bleiler has a way of explaining Powerball odds that really simplifies it. Picture a swimming pool, 40 feet wide, 120 feet long, 5 feet deep, filled to the brim with M&Ms. One single green M&M is hidden somewhere in there. Your job is to reach in, blindfolded, and pull it out. That is roughly the odds of winning the jackpot.

It gets so much worse. For every $1 you put into the Australian Oz Lotto, accounting for every prize tier, you can expect to get back about 50 cents. Very generous. Most lotteries are considerably worse than that.

So why does the global lottery industry generate hundreds of billions of dollars a year?

Because the math has almost nothing to do with why people play.

The Problem With Very Big Numbers

Here is a strange thing about human cognition. Small numbers are fine. The difference between being chased by one lion versus a hundred lions is immediately obvious. Our brains handle that very easily.

Stretch the numbers into the millions and something breaks down. Odds of 1 in 3 million and odds of 1 in 200 million feel the same to most people. Both are really unlikely. Both are vaguely possible. The gap between them, which is enormous in actual mathematical terms, just doesn't register to most people.

Robert Williams, a gambling studies professor at the University of Lethbridge, argues this is simply because humans have never needed to count out 45 million of anything throughout history. We never built the mental hardware for it. So winning the lottery doesn't feel impossible. It feels unlikely. Those are very different things, and the lottery industry lives between them.n

There is also availability bias, which is a fancy way of saying you hear about winners all the time and never hear about losers. Every jackpot winner gets a press conference. The millions of people who bought tickets and got nothing last Tuesday got nothing at all, including news coverage. When you can easily picture a winner and cannot picture the losses, winning starts to feel more common than it is.

The Near Miss Is Not an Accident

Get three numbers right out of six. Notice what happens in your brain.

It feels like almost winning. It feels like being close. A 2009 study found that near-misses activate the exact same reward systems in the brain as actual wins. P. Rogers, writing in the Journal of Gambling Studies, found that near misses, the gambler's fallacy, and a psychological phenomenon called entrapment work together as a feedback loop, each one reinforcng the next, each one making you more likely to buy another ticket.

The thing is, getting four numbers right is not actually closer to winning than getting zero right. The ticket is still worth nothing. Closeness in a random lottery is an illusion. But the brain does not care about that distinction, and the people designing these games know it better than anyone.

The Same Numbers, Every Week

Most regular lottery players pick the same numbers every week. Birthdays. Anniversaries. A sequence that just feels right. And here is where it gets really hard to walk away.

If you stop playing your numbers this week and those numbers come up, you will think about it for the rest of your life. That fear is the gambler's fallacy doing its job, convincing you that a random process has memory, that your numbers are somehow owed to you, that skipping a week could cost you everything.

It is also the sunk cost fallacy. After ten years and thousands of dollars, quitting feels like admitting all of that was for nothing. So you keep going. Not because anything has changed. Just because stopping feels worse than continuing, which is a completely different reason for doing something than actually expecting to win.

The Part Nobody Talks About

This is the piece that usually gets left out of the "lottery is irrational" conversation.

A 2008 study in the Journal of Behavioral Decision Making found that low income people do not play the lottery at higher rates because they are ignorant of the odds or more susceptible to cognitive bias. They play at higher rates because for many of them, the lottery is one of the only accessible mechanisms for a sudden, dramatic change in financial circumstances.

Wealthy people can invest in the stock market, which returns around 7 percent annually over the long run. They can start businesses, access credit, and build assets slowly over time. Someone making $10,000 a year does not have those pathways in the same way. A $2 lottery ticket is not a good investment. But it is the only investment with a real path to financial transformation overnight.

The numbers on this theory are astonishing. People making under $10,000 a year spend an average of $597 on lottery tickets annually, around 6 percent of their income. A 2024 study in the Review of Economic Studies estimated that Americans would spend 43 percent less on lotteries if they were completely free of cognitive bias, meaning a substantial portion of lottery spending reflects something more than just getting fooled. Some economists have started calling the lottery a regressive tax. One that takes the most from those with the least.

So before writing off lottery players as simply irrational, it is worth understanding their situation. The cognitive biases are real, but they are not the whole story.

What People Are Actually Buying

For a lot of players, the lottery is not really about winning.

It is about the two days between buying the ticket and the drawing. That window where winning is still technically possible. For less than the price of a coffee, you get 48 hours of asking yourself what if. A new house. Paying off debt. Walking away from a job that is slowly killing you. The fantasy is real even if the odds are not.

That is hope, priced at $2. And for a lot of people in a lot of situations, that is a completely reasonable purchase.

So Why Does Any of This Matter

The math says you will almost certainly lose, and most people who play know that, roughly. The problem is knowing something and feeling something are not the same thing, and the lottery is very deliberately engineered to exploit that gap.

Near misses keep you coming back. Sunk costs make stopping feel impossible. The gambler's fallacy convinces you your numbers are due. The availability bias makes winning feel like something that happens to normal people. And the whole system is built to hit hardest on the people who can least afford to lose.

The numbers are not hidden, they are right there on the ticket. But numbers that large have never really meant anything to a human brain, and the lottery has always known that.

Enjoyed this post? Numbers in the Wild is all about the math hiding inside the moments you thought were just instinct, from the ticket in your pocket to the odds you never stopped to calculate. More posts coming soon.

Anderson, Ryan. "The Psychology of Why We Play Lotto." Psychology Today, 4 Dec. 2016, www.psychologytoday.com/us/blog/the-mating-game/201612/the-psychology-why-we-play-lotto.

Apollidon Content Team. "Why Do We Play the Lottery? The Psychology Behind Our Obsession." University of Texas Permian Basin Online, 19 Apr. 2023, online.utpb.edu/about-us/articles/psychology/the-psychology-of-the-lottery-gambling-with-our-mental-limits/.

Focus for Health. "The Lottery: The Poor Are Playing, and the Wealthy Are Winning." Focus for Health, 20 Feb. 2024, www.focusforhealth.org/the-lottery-the-poor-are-playing-and-the-wealthy-are-winning/.

Haisley, Emily, et al. "Subjective Relative Income and Lottery Ticket Purchases." Journal of Behavioral Decision Making, vol. 21, no. 3, 2008, pp. 283-295.

Lockwood, Benjamin B., et al. "What Drives Demand for State-Run Lotteries?" Review of Economic Studies, 2024, doi:10.1093/restud/rdae086.

Rogers, P. "Near Miss, Gambler's Fallacy and Entrapment: Their Influence on Lottery Gamblers in Thailand." Journal of Gambling Studies, vol. 14, no. 2, 1998, pp. 111-134, doi:10.1023/a:1023042708217.