To play or not to play: Is that Powerball ticket worth it?
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Trent Hamm Trent Hamm
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 she鈥檇 be better off putting that $20 a month into a savings account, but I might as well be talking to the wall.
Lotteries wouldn鈥檛 exist if they didn鈥檛 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 鈥� 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.
聽The odds of winning a different $4 prize (Powerball plus one number) are 1 in 110.81.
聽The odds of winning a $7 prize (Powerball plus two numbers) are 1 in 706.43.
聽The odds of winning a different $7 prize (three numbers) are 1 in 360.14.
聽The odds of winning a $100 prize (Powerball plus three numbers) are 1 in 12,244.83.
聽The odds of winning a different $100 prize (four numbers) are 1 in 19,087.53.
聽The odds of winning a $10,000 prize (Powerball plus four numbers) are 1 in 648,975.96.
聽The odds of winning a $1,000,000 prize (five numbers) are 1 in 5,153,632.65.
聽The odds of winning the jackpot (Powerball plus five numbers) are 1 in 175,223,510.00.
What we鈥檙e 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.
聽The expected value from the other $4 prize (Powerball plus one number) is 3.6 cents.
聽The expected value from the $7 prize (Powerball plus two numbers) is 1.0 cents.
聽The expected value from the other $7 prize (three numbers) is 1.9 cents.
聽The expected value from the $100 prize (Powerball plus three numbers) is 0.8 cents.
聽The expected value from the other $100 prize (four numbers) is 0.5 cents.
聽The expected value from the $10,000 prize (Powerball plus four numbers) is 1.5 cents.
聽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 doesn鈥檛 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, you鈥檇 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 doesn鈥檛 include split jackpots. Most large jackpots involve two or three groups winning the prize, which splits the amount any one of them wins. So, you鈥檇 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 isn鈥檛 going to happen. Even with a giant jackpot, you鈥檙e 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, that鈥檚 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. That鈥檚 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, you鈥檙e 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. That鈥檚 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, that鈥檚 why. If you see someone playing the lottery, it鈥檚 because they鈥檙e 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 isn鈥檛 playing the lottery because of the investment potential. It鈥檚 pretty easy to see that it鈥檚 a terrible investment. She鈥檚 playing it for emotional and psychological reasons.
Now, is that a good use of money? As an investment, it鈥檚 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 wouldn鈥檛 begrudge her this expense if it bring her some joy and peace. I would only worry about it if she鈥檚 experiencing financial troubles.
