Just last week someone told me the Powerball jackpot had grown to the point that lottery tickets were a “rational” investment.
Assuming a unique winner the Powerball jackpot has to be at least $281 million to make it a rational investment. The more players, however, the greater the chance of a shared jackpot so if there are, for example, 100 million players the jackpot has to be around $400 million to make an individual lottery ticket worth more than $1.
I became sarcastic only after no one could actually answer at what point if any it made sense to take your chances and go with 50 lottery tickets. All I got was “the state is always going to come out ahead!”. At that point I said "even if you had a 2:1 chance of winning $50 or more. Obviously no state would give you 2:1 odds. I didn’t really think anyone would take that seriously. Sorry.
I am very serious about this question: At what odds would it be a reasonable risk to take the tickets and not the cash? How about if someone offered you $50 or 500 tickets with the odds of you winning $100 being 1:1000? Still take the cash because the state always comes out ahead?
Multiply odds of winning times the amount you’d win which is the expected winnings. If the game has multiple prizes then the math gets annoying as you need to calculate the expected winnings of each individual prize and sum them. Then make sure rules don’t allow for multiple winners splitting prizes; if so that complicates it further and you need to figure out the average number of winners of each individual split prize and adjust the expecting winnings for each of them accordingly.
If after all this the expected winnings are > $50 then it might make sense to take the tickets instead of the cash, but there’s another factor to consider.
Now take into account risk aversion. Gambling studies have shown that people tend not to optimize actions because, colloquially, “losing hurts worse than winning feels good.” Because of this you probably need to add a premium. For me I’d say I’d want an expected outcome of at least $55 to take the tickets instead of the sure $50. You’d have to evaluate your own risk aversion.
As I posted above, it isn’t necessarily true that the state always comes out ahead. For some games with progressive jackpots the state will come out ahead in the aggregate but from time to time the prize grows to be large enough that for a given drawing the expecting winnings are greater than the price of a single ticket. This is rare, however, and there are corporations which are formed to watch for these opportunities and take advantage of them.
It’s pretty simple math. You take the expected return and multiply by the number of tickets. If the expected return is 50 cents for every dollar spent, and you were offered $100 dollars worth of tickets, the break even point is getting $50 in cash. If the expected return is 75 cents for every dollar spent then the break even point is $75.
The other day I went down to the convenience store and bought a scratch-off lottery ticket. I won 2 dollars! So I used that 2 dollars to buy 2 more tickets and I won 5 dollars! I used the 5 dollars to buy 5 more tickets and I won 10,000 dollars!!
I thought, “Dammit, now I’m gonna be here all day…”
Same thing happened to me except I kept going. I used the $10,000 to buy tickets and sure enough, I hit for $100,000. I was exhausted but kept going until I won well over a million. I took me forever to scratch those tickets and, wouldn’t you know it, I didn’t win a damn thing.
My wife asked how my day was when I got home. I replied, “It sucked. I lost a buck in the lottery.”
The Powerball rules were changed fairly recently, though. Tickets now cost $2 and the odds are supposedly somewhat more favorable, though I haven’t seen any detailed analysis of them.
Does anyone know what the minimum jackpot would be in order to have a positive EV (albeit with ridiculous variance) under the new rules?
I don’t agree with the “rational investment” part of the academic analysis. It doesn’t matter how good the numbers look if the vast majority of people still lose everything they put in both on that single lottery and over the course of their lives. Even if Powerball type lotteries had a positive expectation every single game, most people would never win and there is nothing rational about that. You have to be in one of the investment companies that buys up massive amounts of tickets before it becomes an “investment” in my mind.
The Massachusetts game I gave earlier was an example or a “rational game”. You could buy up several thousands of dollars worth of tickets and expect to get that and much more back. It was almost certain statistically if you bought enough of them when the timing was right. Some people figure it out and made hundreds of thousands of dollars doing just that.
50 bucks wouldn’t change the quality of my life. Granted, the chance of winning something that would change the quality of my life is small, but I’ll take the tickets.
He ended up with $36,000, the state withheld 28% for taxes. No state taxes here. Before being handed a check, someone also discovered he owed back child support. Deduct another $4000. He is going to buy a new truck (in cash) this weekend.
They were able to publish on that? Wow, standards sure are dropping … I did that just as a back-of-the-envelope calculation ages ago & got $300M as the estimated break-even point. It’s really not that hard a problem to solve.
Just did that same calculation with the new prices and odds–comes out at $287M under the single-winner assumption. So, no significant change–I still wouldn’t think about buying a Powerball ticket with a jackpot of less than $300M.
It was many years ago, but my aversion to gambling cost me some serious money several years ago. Let me explain…
Here in Ontario, there is a pro sports lottery administered by the provincial government. It had been based on NHL, NFL, NBA, MLB and CFL results, and was, in essence, betting on teams to win or lose. They expanded to include results from the English and Scottish premier leagues, which I followed quite closely at the time.
When they expanded to include UK football, they forgot to take into account the time difference. There was a period of several months where the results were broadcast on a show called ‘Soccer Saturday’ by 1PM, and the cutoff for placing bets with Pro-Line sports was 2PM. A group of barhounds had figured this out, (Soccer Saturday even featured ads for Pro-Line Sports!) and were making a tidy profit betting on a sure thing.
Alas, the story made the newspapers when someone from the bar tipped off the Ontario Lottery and Gaming commission, and the cut-off times for bets were changed so that the bets had to be placed before the games started, as with all the North American games. I say ‘Alas!’ because I only found out about it from the newspaper story, having long dismissed lotteries as a tax on innumerate optimists.
So, by all means, examine those lottery tickets in case there has been a mistake, but it would have to be a mistake for it to be profitable. The interest on $50. left in a GIC for a year is much more than any benefit you’re likely to get out of the lottery tickets.
I would take the $50 in cash. I know, I am dull, but at least I know I can actually purchase something I might be keeping…(hmmmm, $50 would be at least 2 Barbie dolls for my collection… :D)