# To play or not to play: Is that Powerball ticket worth it?

(Read article summary)Lotteries exist to turn a profit. If you spend $1 on a lottery ticket, the lottery is going to keep at least some portion of that money. But just how bad a deal is it? Our personal finance analyst weighs in.

Jeannie Nuss/AP

Julie writes in:

I would love to see you run the numbers on playing the lottery. My mother spends $20 a week on Powerball. I keep telling her sheâ€™d be better off putting that $20 a month into a savings account, but I might as well be talking to the wall.

Lotteries wouldnâ€™t exist if they didnâ€™t turn a profit. If you spend $1 on a lottery ticket, the lottery is going to keep at least some portion of that money. In addition, another portion of that money is spent on maintaining the lottery â€“ the machines, the paper, the software, the employees, and other expenses.

How bad is it, though?

The odds on a normal Powerball play are as follows:

The odds of winning a $4 prize (just matching the Powerball) are 1 in 55.41.

Â The odds of winning a different $4 prize (Powerball plus one number) are 1 in 110.81.

Â The odds of winning a $7 prize (Powerball plus two numbers) are 1 in 706.43.

Â The odds of winning a different $7 prize (three numbers) are 1 in 360.14.

Â The odds of winning a $100 prize (Powerball plus three numbers) are 1 in 12,244.83.

Â The odds of winning a different $100 prize (four numbers) are 1 in 19,087.53.

Â The odds of winning a $10,000 prize (Powerball plus four numbers) are 1 in 648,975.96.

Â The odds of winning a $1,000,000 prize (five numbers) are 1 in 5,153,632.65.

Â The odds of winning the jackpot (Powerball plus five numbers) are 1 in 175,223,510.00.

What weâ€™re interested in is the *expected value* of a lottery ticket. In other words, if you buy a *lot* of tickets, how much can you expect to win per ticket?

For example, if you buy 55.41 tickets, you should expect to win a $4 prize. That means that for each ticket you bought, you should expect to win 7.2 cents of that prize, on average.

The expected value from the $4 prize (just matching the Powerball) is 7.2 cents.

Â The expected value from the other $4 prize (Powerball plus one number) is 3.6 cents.

Â The expected value from the $7 prize (Powerball plus two numbers) is 1.0 cents.

Â The expected value from the other $7 prize (three numbers) is 1.9 cents.

Â The expected value from the $100 prize (Powerball plus three numbers) is 0.8 cents.

Â The expected value from the other $100 prize (four numbers) is 0.5 cents.

Â The expected value from the $10,000 prize (Powerball plus four numbers) is 1.5 cents.

Â The expected value from the $1,000,000 prize (five numbers) is 19.4 cents.

In other words, ignoring the jackpot, you should expect an average return of $0.36 on every $1 Powerball ticket you buy.

The lottery grand prize would have to be *gigantic* in order to give you an average return of $1 on each ticket you buy. In fact, the jackpot would have to be $112 million in order for you to get an expected value of $1 on each ticket you buy.

Another problem: **this doesnâ€™t include taxes.** Once you get above the $100 mark, a significant portion of the prize is going to be taken in taxes. If you assume 35% of the prize is taken in taxes for each of those prizes, youâ€™d have to have a jackpot of $194 million in order to have an expected value of $1 on each ticket you buy.

Yet another problem: **this doesnâ€™t include split jackpots.** Most large jackpots involve two or three groups winning the prize, which splits the amount any one of them wins. So, youâ€™d have to win that giant jackpot with no other winners to get a good expected value.

In other words, an expected value of $1 on a lottery ticket isnâ€™t going to happen. Even with a giant jackpot, youâ€™re almost assuredly not going to get an expected value of $1.

But what do you even get with a lottery ticket expected value of $1? You get a terrible investment, thatâ€™s what.

**Imagine you could buy an investment where 31 out of 32 times, you lose all your money.** Even worse, no amount of information can help you figure out which of those 32 times is going to be the winner. Thatâ€™s essentially what a lottery ticket is, even one with expected take-home prizes totaling $1. No one would invest money in that.

In fact, **if the jackpot is less than $100 million, youâ€™re actually better off putting your money into a slot machine in a typical casino.** Most casinos have an expected value of about $0.91 to $0.95 in their slot machines for every dollar played.

If you put your money in a savings account, you keep that dollar and put about one cent in there on top of it each year. Thatâ€™s better than a slot machine and far better than a lottery ticket.

So, **why do people ever play the lottery?** They play it for hopes and dreams, thatâ€™s why. If you see someone playing the lottery, itâ€™s because theyâ€™re dreaming of a situation where they get rich very quickly and thus are able to turn around their current situation in some fashion.

Your mother isnâ€™t playing the lottery because of the investment potential. Itâ€™s pretty easy to see that itâ€™s a terrible investment. Sheâ€™s playing it for emotional and psychological reasons.

Now, is that a good use of money? As an investment, itâ€™s terrible. However, *everyone spends some of their money on something completely wasteful.* If your mother has the rest of her financial house in order and is in a good financial place, I wouldnâ€™t begrudge her this expense if it bring her some joy and peace. I would only worry about it if sheâ€™s experiencing financial troubles.