Ask HN: Expected value of a $2 powerball ticket is now $4.10. Is it worth it? | Hacker News Reader

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.

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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.

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.

> 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.

> 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.

You can tax the pot.

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.

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.

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.

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.

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/

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.

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.

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.

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.

> 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.

I can think of few would like to be rich more than the poor.

Yes but they're not the only ones that play the lotto, not by a long shot.

The point is that going out of your way to say that poor people are the only ones dumb enough to buy lotto tickets is unnecessary.

Nobody calls sports betting a tax on the middle class.

It's called a tax on the poor because they're the ones who often desire it most, while also being the ones who can least afford the luxury of pissing away money. At some point you have to admit there is a deception taking place.

I don't want one chance to win $1.2b...i want 1000 chances to win $1.2m...and there is no lotto in the world offering that.

A startup?

Is there an automated way to buy tickets (online, or whatever)?

A startup could hire someone to buy tickets all day, but that would get tedious...

You can "subscribe" on at least the IL Lottery site to "auto buy" tickets.

There's been a number of instances where people did precisely that--they just sent a bunch of taskrabbits out to buy large numbers of tickets in lots of different locations. Very time-consuming, but still profitable.

there's an app called JackPocket

I think I just understood that the official outlet for lottery tickets physical stores. Is that really so? As a European I am kind of baffled by this, as we (at least in my country) have had an official app for buying tickets for the state lottery and sports betting for ages.

What is the reason for that? Do the players only trust hard physical paper numbers?

Btw, the euro jackpot is about €120m, but still far from profitable.

Yeah there is a startup that does this, they buy lotto tickets for you in app for a fee.

Scratch tickets?

Find 999 friends/coworkers/trusting strangers, pool resources, and split the winnings?

What you want is a raffle, not a lotto. You see those more in Europe (like the massive ones in Spain). Here in the states they sometimes pop up. Illinois used to run million dollar raffles around the holidays. Fixed # of tickets and a guaranteed winner.

Interesting. I guess having a raffle was cutting into the lotto profits?

Raffles are boring. The odds are low. Someone always wins. Lotteries like Powerball are more exciting because the jackpot rolls over many many times. Ticket sales spike tremendously when it gets to levels like this.

Even if the actual EV (money you spend vs. money ultimately in your bank account) were positive, it still might be a bad bet.

If you look at it as an investment, at the very least you have to take into consideration risk and opportunity costs. The risk is enormous, to get 50/50 odds you would need to invest 400 Million. Imagine what else you could do with that money instead, without it being a 50% chance of loosing everything.

I buy them as my "retire earlier" plan. I have disposable income and it doesn't hurt or even make a noticable impact to my lifestyle to spend $40 on it.

We have an even better example of mistaking the numbers for the whole picture. Becoming famous for winning obscene amounts of money greatly increases your chance of being harassed, murdered, or driven to mental breakdown. The expected value of a losing ticket (a chance to fantasize, enjoyment, etc.) is much higher than the expected value of a winning ticket (a lifetime of being hounded for money in increasingly desperate and violent ways).

Someone who knows more about probability say more. Is expectation the right thing to talk about here? I never heard it said explicitly, but if you're talking about expectation, there's some underlying idea that you're going to do the thing many times and add/average the results, right?

Exactly. That is the frequentist interpretation of probability.

In this case it is easy to calculate. Probability to win x Money gained + Probability to loose x money lost.

I thought the insurance companies that underwrite the lotto start buying tickets at this point?

People don't play the lottery because they crunched the numbers (and any number justifying it are likely gamed). People play the lottery in the hope that our shitty lives will be fixed by money.

That's a little harsher than I'd put it - I'd just say that gambling itself has entertainment value to people, which explains why they will, in expectation, pay to do it (see: state of Nevada).

The thing that makes it entertaining is the hope of winning.

Those over 50M jackpots should be divided between n=jackpot/50M winners. (Keep picking matching numbers out of the pool of sold tickets.) That'd keep things more interesting.

600 million cash though so really $2 and that is before taxes which will take about half so more like $1

With the odds of winning at 1:292201338, the expected value of a single powerball ticket is still very much $0. You would need to buy hundreds of millions of tickets to see a positive expected value.

That's not how expected value works.

The expected value is positive.

You're confusing expected value with volatility.

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