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Posted by u/margalabargala 3 years ago
Ask HN: Expected value of a $2 powerball ticket is now $4.10. Is it worth it?
With a jackpot of $1.2 billion, and odds of winning at 1:292201338, the expected pre-tax value of a $2 ticket is $4.10 before taxes, and still profitable after taxes.

If so, are you justifying it with the expected value, enjoyment, or something else?

It struck me that this is similar to the arguments for spending time/money/energy preventing "S-risks", like the very unlikely but very bad possibility of hostile AI takeover or other things talked about in the LessWrong community. Here we have an example of a precisely known magnitude of good that could come about, and a precisely known probability of it happening.

toast0 · 3 years ago
The sum of the annunity payments is not a very useful number. You really need to use the cash value or construct your own present value of the sequence of payments.

Ignoring taxes is also a mistake, because even annuitized, most of the winnings are going to be taxed at the top rate which is approximately 40%.

That said, I'm willing to ignore the tax issue, and I'll generate some numbers and pay my $2 for Wednesday's drawing. The economic utility of pissing away $2 on this may approach 40 cents.

extraduder_ire · 3 years ago
It's probably just because I'm not used to it, but taxing winnings from gambling never made much sense to me. Especially if it's run as a government monopoly.

Taking a cut on the house-side seems way more stable and assured to me, and the numbers are more closely related to what you get. It's a shame the US taxes citizens wherever they are on earth, or I'd expect the done thing to be leaving the country to avoid those taxes, since the money saved would certainly cover it.

I'm sure there's a few accountants around who could come up with a tax minimization scheme that's well worth their cost though. Not here though, national lottery/euromillions are tax free and paid out in one lump sum.

wahern · 3 years ago
> taxing winnings from gambling never made much sense to me.

If you didn't tax winnings, then you're merely inviting a deluge of tax evasion and money laundering schemes. But note that gambling losses are deductible. (You can even itemize your lottery ticket spend.) The caveat is that gambling deductions can only be used to offset gambling winnings; again, because otherwise you're inviting a ridiculous amount of difficult to police fraud.

> Especially if it's run as a government monopoly.

Some states, like California, don't tax state lottery winnings. (But neither do you get deductions for lottery losses.) For other states--at least those with an income tax--I suppose it's just a matter of simplicity to not distinguish state-controlled from private lotteries.

toast0 · 3 years ago
> Especially if it's run as a government monopoly.

It's a state-run government monopoly. The federal government taxes the winnings, but can't tax the state revenue, as state and local government are tax exempt. The company that runs the lottery is taxable, of course, but they're (hopefully) not getting the lions share of the house edge. I know California doesn't charge their income tax on winnings from their lottery though.

The problem with tax minimization on lottery winnings is that you need to do the work before the tickets are valuable. If you make a habit of buying your lottery tickets in a tax advantaged account, then ok; but if you try to move it after it's a winning ticket, that's not going to work well.

toast0 · 3 years ago
As an update, I wasn't able to get my $2 in, but the numbers I generated wouldn't have won. $2 saved to piss away for Saturday.
mikkergp · 3 years ago
Except for ticket splitting right? It’s not exact precision. There’s a non zero chance you’re jackpot is only 1/2 or 1/3rd of the value.
PaulHoule · 3 years ago
For optimal play you want to pick a number which is not popular among other players. On one hand there are numbers (like the lottery winner from last week!) that people overbet. There are other numbers that are systematically underbet.

The "minimax" solution comes very close to having the lottery pick a random number for you, which a high fraction of players (maybe 70%) do. Since so many people are playing quick picks already the benefits of picking an systematically underbet number are greatly diminished, so you might just bet a quick pick yourself.

mint2 · 3 years ago
Expected value here should include some measure or utility. Like “expected value of useful money.”

After the lottery is over 20 million, how much difference does it really make whether it’s 100M, 500M, or 1B.

If there were 1k chances at 1M then I might consider a ticket.

But 1 chance at 1B is about as good as 1 chance at 1M. Unless you’re pooling with several thousand people, Do your expected value at the point where the money’s impact levels off.

tipsytoad · 3 years ago
I wrote an article on an alternative ev metric[1] which takes into account the player having a discrete bankroll (rather than infinite assumed by ev).

https://tompollak.me/blog/ev-v-eg/

skue · 3 years ago
Your odds of winning are no higher with a larger jackpot, and it is only profitable if you win. And unless you plan to invest in a massive number of tickets, the Law of Large Numbers doesn’t apply.
Larrikin · 3 years ago
The lottery should only be played if the amount of money you spend on it could be thrown in a fireplace and not have any effect on your life.

If you want to do something more fun than watch the money burn, then play the lotto and have fun. There's no need to have condescending attitudes about it and definitely don't try to game out the ridiculous odds to justify spending money you wouldn't spend otherwise.

1123581321 · 3 years ago
It is negative expected value because of pot splitting. It came closest to positive EV when the jackpot was around $200-300MM. As interest increases, the number of tickets sold per draw forces the EV downward.

You also need to factor the present value if basing on the annuity and not the lump sum.

DerekBickerton · 3 years ago
The lotto is a tax on the poor. If you are any way mathematically minded, you can calculate the odds and compare it with getting struck by lightning on the top of Mount Everest or being abducted by a UFO. The folly of the lotto still amazes me.
thunky · 3 years ago
> The lotto is a tax on the poor.

This is a common saying, but it's a backhanded exaggeration.

Maybe more accurate to say it's a tax on those that want to be rich.

soulofmischief · 3 years ago
I can think of few would like to be rich more than the poor.