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That's probably true. They should try to educate people that if there are 250 times as many winners that your chances of winning a significant amount of money is much higher.

People aren't betting that way because they're uneducated. People generally don't play the lottery because it's statistically wise. They play because dropping $1-3 on a ticket is no big deal, and it provides a little excitement and lets them fantasize about the winnings. Fantasizing about what you'd do with $250M is a lot more exciting than fantasizing about what you'd do with $1M, and once the odds are low enough, any emotional investment in the math is going to be lost in the rounding error.

> and it provides a little excitement and lets them fantasize about the winnings

I've heard this before, but why do you need a ticket to fantasize about what you'd do with that much money? It can be a conversation starter and I can see the excitement aspect in watching your numbers come up (if you don't have a hundred combos to watch at once), but fantasizing is free.

As someone who's bought a few lottery tickets in his life, I can confirm that the fantasizing is in fact better when it's about something that could happen to you.

you could also just happen to find a winning lottery ticket on the street.

the likelihoods of the two events are similar, and one fantasy is free.

Have you tried buying a lottery ticket? It sure feels a lot different than the "free" variety you're proposing.

And props to you if you're a true rationalist who derive nearly equal amounts of satisfaction from both fantasy events, but most people don't behave like that.

The likelihood of the two events isn't at all similar. How often do you find discarded tickets for future drawings on the street?? You're much more likely to find one (or ten, or a hundred) if you buy them. Then once you're in possession of said tickets, now the odds of winning are the same.

Have you ever bought lottery tickets?

> The likelihood of the two events isn't at all similar.

1e-9 and 1e-100 should both round to 0.

and since people spend all sorts of time imagining things with likelihood _0_ (or downright counterfactual!), 1e-100 should be plenty to get you rolling.

> How often do you find discarded tickets for future drawings on the street??

you're already fantasizing a wildly improbable chains of events (buy ticket, win max amount, and then, unlike a huge number of winners avoid having your entire life ruined by it), but imagining finding a piece of paper on the street is a step too far?

and if "found it on the street" is _really_ the problem, you could always choose to fantasize that someone gives you a ticket, or even just pretend that you purchased a ticket. (that's hardly improbable, after all.)

It sounds like you fundamentally just don't understand the psychology of people who buy lottery tickets.

That's fine, then don't buy them yourself, but it makes no sense to argue against other people's actual experienced feelings and thoughts. You can't use logic to "win" this.

> You can't use logic to "win" this.

and yet here you are, producing justifications about how your fantasy has to have particular levels of believability, instead of just saying "i like doing it".

The probabilities differ by less than 0.0000001.

You could have a rich uncle in Scandinavia about to die and leave you $200M

I think if you could educate people on their expected return from a lottery ticket purchase, they wouldn't play at all.

Telling people that they have a 95% chance of winning nothing at all is not a good way of selling lottery tickets.

I think it's naive to value a lottery based solely on your monetary expected value. The value of money doesn't increase linearly, and isn't the same for everyone. $20 could have an inconsequential effect on my quality of life, while winning say $2 million could be a total life changer.

Likewise, the difference in impact between winning $0 and winning $2 million is likely a lot larger than the difference between winning $2 million and winning $4 million. So a straight EV calculation doesn't really tell the whole story.

There's also the entertainment value of participating in the lottery to consider, even when you win nothing.

Personally I like to think of lotteries as a binary thing - either I win enough money to retire now, or I don't.

I think there's more nuance than that. Winning enough to pay most of your house off wouldn't necessarily let you retire but it'd make you a lot more comfortable, for instance.

I have a graduate degree in maths and have played the lottery. The expected return isn't the point.

Expected return may be helpful but imo not sufficient without variance. Some cumulative jackpots are large enough that the expected return is actually profitable but the probability of actually hitting the numbers is vanishingly small.

However, even with positive expectation value, you should not always play. One should first check the Kelly criterion, which is well explained Russel O’Connor’s blog post:

“Do Not Play the Lottery Unless You Are a Millionaire” http://r6.ca/blog/20090522T015739Z.html

If the lottery was in the business of educating people, they would lose their customer base.

I know that this is true, but if you have a good blog post explaining these statistics i'd appreciate it!

The odds are low enough that multiplying by 250 doesn't make much of a difference.

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