Powerball is always -EV

[EverettKings]

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Not only is paying the buck for the lottery fantasy entertaining ... spending $1, or $5, to enter the powerball is money I will essentially not even notice missing. So there's basically NO downside to playing, for me personally.

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I agree, I spend $1 every drawing when it is over $100 mil. the 5 minutes I get in the shower each morning thinking of how I will quit, and what sort of special sex room I will have in my new house makes it money well spent.

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Maybe you guys missed the part where I said:


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On the other hand, if you get $1 in entertainment from playing by daydreaming for a while what you'd do if you won, then the odds don't matter at all.

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[EverettKings]

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reminds me of a fun game:

you pay me $X to play, and I give you a fair coin. If you flip heads, I put $1 in the pot and let you flip again. Every time you flip heads I double the money in the pot and let you flip again. If you flip tails, you get the money in the pot and the game is over. What is a fair value for $X?

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$2.

I am not willing to gamble on flipping more than 2 in a row. I think you would end up pretty even at that.

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Wrong.

Answer in white:
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I will pay you infinity dollars

E(game) = 0*(1/2) + 1*(1/4) + 2*(1/8) + 4*(1/16) etc = the sum of an infinite number of 1/4s. </font>

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Okay, let's play then.

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Sorry. I wouldn't pay infinity dollars. The fair value in a strictly mathematical sense is infinite, which is the question that I was trying to answer.

How much would I actually pay? No idea. I'd have to sit down and figure out a function for the value of various amounts of money to me, and then figure out the true value of the game. $2 seems too little, but I don't feel like grinding numbers to pick a real value.

[ilya]

I think your argument is kinda cheap. It exploits the well-known and irrational psychological tendency of people to take the short end of the EV stick to lock in a profit.

Also I think saying that each million is worth less than the last one exploits a similar psychological illusion. In reality I think each extra million should be worth more than the preceeding one, because of the additional leverage it gives you.

[gumpzilla]

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How much would I actually pay? No idea. I'd have to sit down and figure out a function for the value of various amounts of money to me, and then figure out the true value of the game. $2 seems too little, but I don't feel like grinding numbers to pick a real value.

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I actually did this once for a couple of different utility functions. One, I think, was that the utility of money went like the square root of the money involved. In that case, I think the amount you should pay is something like $100. I also considered a logarithmic utility function; there it's closer to $20, if I remember correctly. It's been a while, but those were the approximate numbers. They seem much closer to what most people would answer, I think.

[bobman0330]

I think you must be right. If it was really +EV, you'd expect to see JPMorgan or some big private equity fund snap up $50 million of tickets. That would also be a lot more tax-efficient.

[EverettKings]

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I think your argument is kinda cheap. It exploits the well-known and irrational psychological tendency of people to take the short end of the EV stick to lock in a profit.


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It is 100% rational sir.

I would much rather live have two lifetimes with $50 million than one lifetime with $200 million. The extra happiness for the first 50 million is significantly more than the extra happiness of the next 50 million. It is a matter of translating $$ to utility/happiness, and it's not a linear function (see gumpzilla's post, or google 'Utility of Money').

[Lottery Larry]

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I think you must be right. If it was really +EV, you'd expect to see JPMorgan or some big private equity fund snap up $50 million of tickets. That would also be a lot more tax-efficient.

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Let's see someone fill out and submit 145M tickets. Don't make a mistake, because the karma gods will be sure to pick that combo of numbers.

[NajdorfDefense]

who are the nits that would take $1m over a 50% chance at $410mm? That's [censored] insane.

[Black Aces 518]

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who are the nits that would take $1m over a 50% chance at $410mm? That's [censored] insane.

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I would. $1M would change my life. Also, I run at about 16% on coinflips, so you have that.

[hmohnphd]

To paraphrase one of my math professors, it's silly to look at EV of the lottery unless you're playing it so many times that winning it one more time is not a big deal to you.

Yeah this doesn't have anything to do with the point of your post, but it just bugs me when people talk about the EV of the lottery. Like if it was slighty +EV people would be buying wheelbarrows full of tickets or something