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.
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.
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.
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.
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.
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?
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.
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.