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Comment by islewis | Hacker News Reader

Can someone explain to me how the EV can be so incredibly low? I know the answer is because people will buy the tickets no matter what, but even compared to other losing games the lottery comes away looking like an absolute bandit.

A run on the simulation (n=1000000) comes back with -92% EV. It looks like -10% [1] is a rough estimate for slot machine EV, which I would ballpark into the same game genre (-EV, no skill entertainment) as the lottery.

What accounts for this payout discrepancy in what I would consider similar games? On that train of thought, what prevents a new lottery from coming in and offering a _generous_ -50% lottery, offering ~5x as much money as before?

[1]* https://www.888casino.com/blog/expected-value

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Because you shouldn't use the simulator to calculate the EV, or said differently your n=1000000 is too small.

Assuming you used the first lottery example (Mega Millions), the EV is easy to calculate directly and is -$0.66/ticket, ie -33%

The jackpot is a whole $1 of that EV! Without it, the EV is -$1.75/ticket, ie -87%, which is closer to what you got in the simulation.

Exactly.

In short, the simulator doesn’t buy enough ticket-draws to approach the Law of Large Numbers.

But that’s also a feature of the lottery — most people overestimate their ability to win or underestimate how many lifetimes of consistent play is required to statistically win a jackpot.

I don't think people actually make that mistake. They know the chance of winning is tiny. The point is more that a non-zero chance of life changing money (plus the entertainment of fantasising about a win) is worth more to them than the cost of the ticket.

Exactly, winning the lottery is massively life changing. This is actually something I think people don't understand about the psychology of lottery. In some regards it doesn't matter if the money is $50M or $500M for most players even though that has a huge impact on the EV.

this was my approach when i lived in oregon. i played the state lottery which was something like 20x better odds, granted the jackpot was usually like $6 million after cash out, but that was still totally good in my book. it cost a buck and i got to have fun with the idea of it for a few days.

one time i get like 20 weeks in a row up front (a post-dated ticket) and i won $56 dollars or something one week. i did the odds of that happened and it was something that would happen like once every 30 years if i played weekly. i stopped after that, haha.

>On that train of thought, what prevents a new lottery from coming in and offering a _generous_ -50% lottery, offering ~5x as much money as before?

federal-level gambling syndicate isn't something that a private party can easily jump into.

so the answer is : a mix of 'grandfather'd-in' and protectionism, if we're talking U.S. here.

> What accounts for this payout discrepancy

Mega lotteries draw once every 2-8 days. Slot machines / video poker / etc are happy to draw as fast as you can push the button. They are designed to take your money, but their rewards systems are completely different.

Also, the mega lotteries benefit from viral marketing, “earned media”, and water cooler talk. Slot machines are just a way for bored people to pass the time, much like video games or doomscrolling.

In the US at least they're a state monopoly

Because a lot of the proceeds go to school districts.

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