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On the very rare chance that I purchase a lottery ticket, it's almost always when the jackpot grows to an enormous sum that starts making headlines. I don't do this because of a cost-benefit analysis or anything like that. I don't expect to win regardless of the prize. I buy a ticket for fun. For a few days, I entertain the fantasy of winning & joke around with friends about the things I would do with it all.

This is a perfect example of how the “rational agents” theory breaks down. From a mathematical POV what you do is clearly irrational, yet as a human it is perfectly sensible to do what you do, spend a couple of $$, have a bit of fun and move on.

Why isn't it "rational" to purchase entertainment products you enjoy? Do you think economists actually rely on the axiom that humans are born with a perfect ability to play logic and probability games?

> From a mathematical POV what you do is clearly irrational

The ticket costs the same whether the pot is small or large. For every lottery, there is a jackpot amount at which the expected value of a ticket exceeds its cost. Some lotteries occasionally approach this, even after taxes, although the chance of sharing the pot complicates that.

Why is it "clearly irrational" to buy a ticket only when the EV is closer to 1, rather than when it's something like 0.2?

>I don't expect to win regardless of the prize. I buy a ticket for fun.

Plenty of pleasant brain chemicals and time daydreaming for the low low cost of a couple bucks.

It’s transactional entertainment, no different than dropping $2.99 to watch an old episode of Law and Order on Prime Video.

Harmless fun for those who can afford it.

When the jackpot would get really high for the Powerball I'd set a meeting for me and a few coworkers. We'd go across the street to a bodega to get a ticket or two and sit in the park for a bit to talk/argue about what we'd do with the money. We'd all return to the office happier despite knowing we obviously wouldn't win.

Something important to understand about gambling is that the entertaining part is not actually the prize, but the uncertainty between pulling the arm and getting the result. Buying a 20 dollar ticket to dream about a billion dollars for a day isn't a horrible use of money - it's just like any other form of entertainment. It only becomes a problem when people are addicted to that feeling of uncertainty.

Was going to say this. People pay for a lottery ticket to dream about what their life could be like if they won (similar to people who never launch that buiness idea). Many people derive a lot of happiness from this, moreover (in the uk) a large proportion of the takings goes to good causes and people generally accept it is extremely unlikely they will win but instead of just donating to charity they at least have a slim chance of a massive gain.

Bah. Plenty of uncertainty guessing consumer confidence, inflation, and banks' and the Fed's monetary response.

How much should I invest, save, or spend?

It's a continuous game with your life savings at stake.

The lottery is an accepted tax on math morons, as my old teacher liked to say.

And people have "learned" that and somehow think that when the expected return goes "positive" that it somehow isn't silly anymore.

I would be interested to see it change so the jackpot doesn't go UP each time, but instead the number of winners goes UP somehow - perhaps by drawing an extra powerball if nobody has won for a certain period.

The absolute sad part of it is the large percentage of people who play and shouldn't; you rarely see the well-off playing, but you will see poorer people playing (which makes some sense, Bill Gates winning wouldn't change him at all).

Even sadder is what happens to the winners on average; the winner is often someone not good with money and they get given a large amount of the thing they're not good with.

> The lottery is an accepted tax on math morons, as my old teacher liked to say.

There is a difference between zero and a non-zero chance of winning, even if you hold just one ticket. Even if the probability is low, it's non-zero nevertheless. Someone always wins.

> I would be interested to see it change so the jackpot doesn't go UP each time, but instead the number of winners goes UP somehow - perhaps by drawing an extra powerball if nobody has won for a certain period.

This is more or less the concept of the lottery game with the MIT group stories.

Once the accumulated prize pot hit a certain number, the pot would 'roll down' to all winners on that drawing. So, the meta game was to buy as many tickets as possible for a rolldown drawing. And then, to buy as many tickets as possible for a near rolldown drawing to force it into rolldown, perhaps without other buying groups noticing. Of course, this meta game turns this type of drawing into less of an 'everyone can win' thing and more of a those with resources can work the odds and come out ahead; which is contrary to the preferred public image of the lotteries.

On the traditional lotteries, you do see that the large jackpots tend to have more cases of multiple jackpot tickets.

> The lottery is an accepted tax on math morons, as my old teacher liked to say.

This glib old chestnut falls apart when you ask the "math savvy" what the probability of winning is when a person buys more than 1 ticket. Probabilities are unintuitive here (albeit simple) such that most people are "morons".

Even then the whole thing breaks down because the chance of winning is so astronomically small

Even sadder is what happens to the winners on average; the winner is often someone not good with money and they get given a large amount of the thing they're not good with.

You don't need to be particularly good with money if you have more than you can ever spend.

It's been demonstrated to be quite possible to outspend lotto winnings.

To start with, the headline numbers are usually the sum of the annuity payment option, cash value is 50%, federal tax rate is close to 50%, so you only really get 25% of the headline.

Then people spend a bunch of money on extravagent gifts for family and friends and themselves; then it's time to take bad loans and make bad investments. A couple million here, a couple million there, pretty soon you're talking about real money.

Well managed, a much smaller sum would be enough for a nice life with no money stress, but it's demonstrated possible to overspend it to bankruptcy.

Most big lotto wins are in the seven to low eight digit range. You can absolutely blow away that amount of money in just a few years, and there are dozens of examples.

Funny, I took this comment in pretty much the opposite way. As in people on high incomes are probably kidding themselves about what good money managers they are - the stakes are pretty low when you get another 5 or six figures dunked into your account regularly.

Single parents raising a few kids on minimum wage? That requires some real financial planning

That may not be that "hard" if you simply don't spend money you don't have. But now everyone has easy access to credit so it's harder to keep your income below your expenses without careful calculation and work.

I do believe I just got told that having a high income and access to easy credit makes it harder to manage your money than living on the poverty line.

God, I love this site.

Off the top of my head, Evelyn Adams. Won the lottery twice, thirty years later she had blown through it all and was living in a trailer park.

It's not that hard to spend $200M. Charted private jets are expensive. Rolls Royces are expensive. Multiple $10M homes are expensive.

You're correct. Buying a powerball ticket doesn't measurably change your chance of winning.

But you're using an argument based in mathematics to try and convince people who either don't understand or understand but choose to ignore it. In essence, the facts you've chosen to present aren't relevant to convincing those individuals.

> Buying a powerball ticket doesn't measurably change your chance of winning.

This doesn't feel right. There must be a statistical difference between zero chances of winning and 1 in a billion chances of winning. Close to imperceptible maybe, but zero is pretty absolute.

Do you fear being struck by lightning (about 1 in a million)? Being attacked by a shark at the beach (about 1 in 4 million)?

Do you panic a little bit every time you step outside? Or get into the water?

Both of those events have a way higher chance of happening than any single person winning the lottery (1 in about 292.2 million). We don't panic because the chance of being struck by lightning doesn't measurably increase when we walk outside.

The difference between 0 and 0.000000003 is insignificant. A foot is 12 inches. A foot and 0.000000003 inches is also close enough to 12 inches that it doesn't matter to record the inches. Lego bricks have a tolerance of about 0.001mm.

That's what they mean when they say there is no measurable change. There's technically a change, but it's not a change that means anything.

> Do you panic a little bit every time you step outside? Or get into the water?

I wouldn't say panic, but I am aware of those things and do my best to prevent them from happening to me. If they were guaranteed to happen to somebody each Saturday at 8pm I would be a little more nervous around that time.

> The difference between 0 and 0.000000003 is insignificant.

Surely this depends on the unit of measurement? If I told you the train station was only 0.000000003 parsecs away would you be happy to walk?

My point is that the original statement is only true if nobody ever wins the lottery. But line up all the people who have won. What do they have in common? They bought a ticket. Line up all the people who have never bought a ticket. What do they have in common? They've never won.

Nobody's saying the odds are good or that the lottery is a sound investment strategy. But zero in infinite chances seems measurably less than 1 in 292 million.

No. You don't. You generally aren't aware of them either. I'm comfortable saying that. Don't get so entrenched in a position that you find yourself saying ridiculous things just to defend a bad point.

The lottery also isn't guaranteed. The lottery goes unwon often. And it doesn't change the odds.

You should be way more afraid of both lightning and sharks if you think buying a lottery ticket gives you much more a chance of winning it than me.

And you know what's crazy? 0.000000003 parsecs is just about 60 thousand miles. On the scale that parsecs are measured, that's nothing. It's a rounding error. It's telling that you have to use cosmic scales to make the difference measurable. That should tell you something.

Line up all the people who have been struck by lightning, what do they have in common? They went outside. So never go outside.

Conversely, line up all the people who bought tickets and never won. There's far more of them. You are more likely to get cancer than win the lottery. So much more likely that buying a lottery ticket at a gas station is irony of the highest order. Due to the number of known carcinogens found at gas stations.

Please don't tell me what I am aware of based on what you choose to ignore. I have moved off golf courses during lightning storms because I knew that I was creating conditions likely to increase my odds of getting struck. I have swum closer to the shore because I know that out in the colder waters past the breakers is where shark attacks happen and because I live in a country where 4 people get attacked (one fatally) in shark attacks every year.

And if either of those things do ever happen, I can guarantee that my last words won't be "but this was statistically improbable!!!"

I agree, it's unlikely. You don't have to wheel out numbers about how unlikely winning the lottery is either. But I know that my chances of getting attacked by a shark in the Costco car park are the same as my chances of winning the lottery without buying a ticket: zero. And if we can't agree that zero is different to one we'll just have to agree to disagree.

I said "measurably". That is to say it has no impact on your life, other than reducing the amount of money you have.

Anyone who took a basic combinatorics or discrete math class can explain the mathematical difference, which is obviously nonzero.

Well if we're changing the statement so that it's now about impact on life that's mostly correct, except if you're talking to the person who bought the winning ticket.

But we were originally discussing if buying a ticket changed your chances of winning.

Not buying a ticket you have zero chances in infinity. Buying a ticket you have 1 chance in 292 million. I don't think it matters that you have decided that 292 million is a really big number. It's certainly less than infinity and 1 is certainly more than zero. I don't know what kind of maths classes you would need to take to see what has changed there.

Hence the annoyance. Doubly so when they claim to acknowledge the facts but buy the ticket anyway.

Aren't there situations where a lottery's prize makes a ticket puechasr plus ev? Hence the practice of some people forming big ticket purchasing collectives and pulling profit from these situations. Probably a very uncommon circumstance and conditional to the design of the lotto

But EV isn't everything, skew and volatility also determine price or value. No +EV is worth $1,000 ticket for a single 0.0000000000001% chance of a bajillion dollars.

Your post is spot on. I think my parents called it 'dream tax'. Looking back, I am inclined to agree.