The Mathematical Case For Buying a Powerball Ticket

HughPickens.com writes Neil Irwin writes at the NYT that financially literate people like to complain that buying lottery tickets is among the silliest decisions a person could make but there are a couple of dimensions that these tut-tutted warnings miss, perhaps fueled by a class divide between those who commonly buy lottery tickets and those who choose to throw away money on other things like expensive wine or mansions. According to Irwin, as long as you think about the purchase of lottery tickets the right way — purely a consumption good, not an investment — it can be a completely rational decision. "Fantasizing about what you would do if you suddenly encountered great wealth is fun, and it is more fun if there some chance, however minuscule, that it could happen," says Irwin. "The $2 price for a ticket is a relatively small one to pay for the enjoyment of thinking through how you might organize your life differently if you had all those millions."

Right now the Multi-State Lottery Association estimates the chances of winning the grand prize at about 1 in 175 million, and the cash value of the prize at $337.8 million. The simplest math points to that $2 ticket having an expected value of about $1.93 so while you are still throwing away money when buying a lottery ticket, you are throwing away less in strictly economic terms when you buy into an unusually large Powerball jackpot. "I am the type of financial decision-maker who tracks bond and currency markets and builds elaborate spreadsheets to simulate outcomes of various retirement savings strategies," says Irwin. "I can easily afford to spend a few dollars on a Powerball ticket. Time to head to the convenience store and do just that."

Comments

I'll take the wine instead

[fish waffle]

I still maintain that by not buying a ticket my odds of winning are not significantly reduced.

Re:I'll take the wine instead

[GrandCow]

Incorrect. Buying a *single* ticket is worth it, since it puts you on the playing field at least. It's buying 2+ tickets that aren't worth the money, Every ticket after the first raises your chances by such an incredibly small amount that it's not worth it. The first ticket raising your chances above a flat zero is worth it though.

A tax on stupidity

[yelvington]

I figure the lottery is a tax on stupidity. And if it goes to $500 million I'm easily ten bucks' worth of stupid.

I always keep

[jd2112]

An unchecked lottery ticket in my wallet. That way i am both potentially broke and wealthy at the same time.

Pure expected value analysis misses the point

[Anonymous Coward]

The expected value of a gamble being positive does not necessarily mean it is a good idea for a limited human.

Consider, for example, a lottery which cost $50K to enter, and returned 10e80 dollars with probability 1 in 10 billion.
Expected value dictates that it's an absolute home run, but 99% of individuals would not take that bet, because with near-certainty it will bankrupt them.

Similarly, for most, a $1 bet for a $1M jackpot with 1 in 1.1 million odds (e.g. negative EV) is better than a $1 bet for a $10M jackpot with 1 in 9.9 million odds (e.g. positive EV).

Why? Because of the nonlinear value money has to an individual.

Re:Another silly decision

[afidel]

The CRA did NOT cause the financial crisis! This has been debunked many times. In fact in ~75% of communities CRA loans had lower default rates through late 2009 than traditional conforming loans (let alone crap like interest only, sub-prime, and liar loans) due to more stringent underwriting criteria. No, the cause was improperly rated securities comprised of crap that was sold in bundles to the big banks and through the back door to Fannie and Freddie.