Comments by "EebstertheGreat" (@EebstertheGreat) on "The Biggest Lottery You've Never Heard Of" video.

It is ungoogleable. No matter how I phrase my query, google refuses to believe I want anything except dozens and dozens of articles in a row about the largest lottery jackpots ever awarded.
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I'm not sure it's that unintuitive. Instead of probabilities, imagine every combination is realized in practice, so we're just talking about fractions of some actual group. Then the "expected value" is just an average over the population. So if we give, say, 1/4 of the group $1 prizes and 1/3 of the group $2 prizes, then clearly the average prize earnings are (1/4)($1) + (1/3)($2) = $ 11/12. And it doesn't matter how much those groups overlap, because we are just interested in the total amount of money doled out. So it is with expectation. Who cares whether the winners are packed together or spread out? It's about average winnings. So just add the value of each prize.
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@AntonioLasoGonzalez Yes, but the page doesn't cite any source. Anyway, the idea is to find it without putting the answer in first. Like, if you don't already know which lottery has the biggest payout, how do you find it?
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Yes, that's a consequence of linearity of expectation. Add up all the prizes paid out and divide by the number of participants. It doesn't matter to whom those prizes are distributed (i.e. how many people win multiple prizes). But this approach isn't useful in some lotteries where winning a higher prize precludes winning a lower one, because calculating the total amount paid out is just as hard as calculating the expected value. (In fact, it's basically the same calculation.)
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@oro5421 Yeah, if you know that number, you can just divide by the number of tickets printed. (That "prize fund" figure represents what they will pay out if every ticket is sold and every winner claims their prize.)
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@FuoChEsplode Yes, his calculation of the probability of winning "something" is flawed. What he actually calculated is "the expected value of the number of prizes you win minus one." Someone who wins two prizes is counted doubly in that calculation.
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@AnotherRoof The top-line figure they advertise online is the entire prize pool. They advertise it right next to the top prize of the Euro Millions, which is only half its prize pool. Tiny text points out the difference, but I still think that's skeevy. It doesn't help that media refers to it as "el gordo," even though that's actually just the top prize. That said, most ads for the lottery don't seem to emphasize the size of the prizes as much as they do in the US in general. And I doubt anyone is confused enough to think the top prize is 2.7 billion euros (though idk, maybe some do). You also claimed that these tickets are only sold in official lottery shops, which is false. It's sold in many unlicensed shops around the country, and licensed, privately-owned-and-operated shops also sell them. Your numbers are also a year out of date. In 2024, 193 series of tickets were sold. It was 185 in 2023 and 180 in 2022.
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The word "lotto" is actually the origin of the word "lottery." The 15th century Milan numbers game was called "Lotto," and the word was also used for other sorts of gambling in large pools with large prizes in Italy. The French got the word "lotterie" from the Italian "lotteria" from "lotto" + -"-eria," and in turn the English got the word "lottery" from the French (unless we got it directly from Italian; it's hard to tell). I'm not sure why in modern French and English, we use the -eria/-erie/-ery suffix instead of just the original "lotto." At any rate, all versions ultimately derive from "lot," as in the object one draws to decide a random outcome. All English meanings of "lot" ultimately come from that object (e.g. a straw).
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@LightPink He spent three videos and two hours proving 2 + 3 = 5. He is not assuming a high-level understanding from his audience.
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Your Powerball calculations assumed that each jackpot winner would receive $246 million. But when the jackpot gets that high, many people play, so the probability of sharing the prize becomes substantial. In the Powerball, if multiple people simultaneously win the jackpot, the jackpot is evenly split between them. So really, the expected value of your ticket is less than you stated (particularly if you choose commonly-played numbers). On the other hand, sometimes the jackpot is more than twice that size, so in those rare cases, a ticket could really have a positive expected value . . . before taxes. Because once you realize that state lottery winnings in the US are subject to federal income tax, it becomes practically impossible for such a scenario to occur. In most states, even state taxes can apply, in spite of the fact that it is the state itself paying you your winnings. And it's actually worse than that, because in the US, lottery jackpots are not paid as lump sums but as escalating monthly payments. The present value of the annuity is not really as high as they claim, so you actually get much less than stated. IMO that should be illegal, since it is literally, factually untrue, but that's how it is. (Of course, once you consider a more reasonable logarithmic utility function, it becomes even more stupid to play the lottery, since each dollar you risk losing today is a lot more valuable to you than each dollar you win at the end of your hypothetical large jackpot. However, this utility calculation doesn't apply the same way to lottery pools.)
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@AnotherRoof Thanks, I wasn't sure where the figure came from, but that analysis looks pretty good.
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@alexmcdonough4973 At least if you trade stocks, you incidentally also own stocks, and owning stocks produces a return (in dividends, and often growth). So you might earn a profit by mistake. And the expected value on day trades is just 0. But gambling at a casino, or much worse a lottery, has a massively negative expected value with no upside. At least at a casino, you can spend some time playing games and try to justify the expense as entertainment. With a lottery, all of your enjoyment is packed into like thirty seconds of anxious hopefulness while the numbers are drawn. (Or I guess if you are Spanish, four hours of agony while children slowly sing numbers that you might match.)
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