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Comment by mattheww | Hacker News Reader

FYI, if you make a realistic calculation (including tax and multiple winners), the EV of a lottery ticket is still negative.

Depending on your tax bracket, the non-jackpot prizes have about $0.19 of EV.

In a state where you don't pay tax on lottery winnings, like CA, you cash option post-tax is currently estimated at $408,403,045.

My estimate of the multiple winner correction to the EV is 0.8, based on numbers of winners for prizes >$500M.

Your jackpot EV is therefore $1.08 and the total winnings EV is therefore $1.27, meaning the overall EV is -$0.73.

For there to be positive EV, that delta needs to all come from the jackpot, so the headline jackpot number would need to go from $1.1B to $1.8B to get it there.

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Great analysis. I want to share my thoughts on EV because they seem to go against what pretty much everyone else is saying. I think even if the EV was >$2, it would still be irrational to play. I say this because I think it's silly to talk about the EV of buying a single ticket when the odds of winning are 1 in 300 million.

Like, you still aren't going to win the jackpot. Your odds didn't improve just because the jackpot got bigger. I guarantee you are going to find out tonight that you wasted $2, just as you would have wasted $2 at any other time when the jackpot is/was smaller.

I think it's just people rationalizing what they know is an irrational behavior. They're fooling themselves into believing they are making a rational choice because they want in on the fun/excitement despite paying the "poor tax."

Anyway, good luck to anyone who decided to buy a ticket and enjoy a few hours of fantasizing about what you'd do with the winnings :)

You could flip the perspective and look at it as helping out the winner.

Still for most people, their biggest return is being able to day dream for 5 minutes what it would be like to win.

Totally. And it becomes a cultural phenomenon - neighbors and coworkers are chatting about it … you want to be part of that moment. Here’s what I wonder - what is the maximum frequency of big media hyped jackpots? Would we all do this again next week, next month? I don’t think so. Maybe next year?

They say you can't win if you don't play (pay). But that's not true! There is an epsilon chance that someone dropped their lottery ticket and the wind blew it away and they gave up in getting it back and while taking your groceries to your vehicle in a parking lot it blows by you and you pick it up. And there's an epsilon prime chance that it will be the winning ticket. So there is an epsilon times epsilon prime chance that you win the lottery without actually playing (paying inti) it. ;)

I like to say that your odds don't significantly change if you pay for a ticket or not. Both non-zero but very close.

Most of what you're describing is captured by the Kelly Criterion: it tells you the "optimal" fraction of your bankroll you should bet to maximize returns given the odds and EV. For a game with positive EV and 1 in 300M odds, you should be betting a very small fraction of your overall bankroll -- well below $2 for anyone not already in the 0.01% wealth bracket. So indeed, it would be irrational (suboptimal) to participate in the lottery unless you were already very wealthy.

Even beyond the Kelly Criteria, you could also tweak your EV based on the marginal utility of a dollar -- i.e. going from $0 in savings to $10M would have a massive impact on your quality of life, whereas 10x'ing from there ($100M) would provide marginal additional benefit comparatively. Thus, (ignoring Kelly) the "quality of life EV" for a $10M jackpot with 1 in 5M odds is vastly better than a $100M jackpot with 1 in 50M odds despite having the same EV.

https://en.wikipedia.org/wiki/Kelly_criterion

Nice, I had heard of the Kelly Criterion before but never thought to consider applying it to this situation. It's fantastic if the mathematically correct amount to wager (for any ordinary person) is less than $2 which rounds to 0 tickets which supports my intuition to not play.

Your second paragraph touches on another thought I had, which is why people think it's only worthwhile to play when the jackpot is $600M+. Any of us would be happy to win just $20M so why not play for every jackpot? Again it comes down to that misleading EV calculation, which I believe doesn't even matter if you are only going to buy 1 ticket only. Wagering based on the EV would only make sense if it was feasible to buy on the order of 100M tickets. Then you'd have a reasonable shot of winning each jackpot. And playing enough jackpots, you would come out ahead.

About a decade ago Megabucks in Wisconsin (a Wisconsin State pick six game) had a positive EV after taxes were even taken out. I think it was maybe a penny at best. However, buying more than one ticket is still foolish in my book. 1 in 14 million vs 1 in 1.4 million vs ... They're all ridiculously long odds. You more likely to die driving to get your ticket.

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