No, it’s not mathematically advantageous to play powerball (but that doesn’t mean you shouldn’t play).
A common quip about the lottery is that it’s a tax on people who are bad at math. Whether or not you agree with that, this time could be an exception. You have probably heard that the Powerball jackpot is at a record high of $1.4 billion. This has prompted articles and blogs claiming that, just this one time, it’s mathematically advantageous to play the Powerball.
The logic goes like this:
The mathematically calculated expected value of a $2 Powerball ticket at this current level is more than $2. In other words, the odds are in your favor. How could that be? The expected value of any bet is the probability of winning times the potential winnings. Think of it this way, let’s pretend you could bet on a coin flip. Heads, you win $10, tails you lose. The expected value of that bet is $5. Assuming a fair coin, if you made that bet a thousand times, you would expect to win $5,000 (500 heads x $10). Understanding that, if you could participate in this wager with a bet of less than $5, you should take that bet. If you had to ante more than $5, you should sit it out.
Now then, here’s the math with the head-spinning $1.4 billion jackpot. Your odds of winning are 1 in 293 million. At $2 per ticket, the jackpot would need to be at least $586 million for the expected value to be equal to the cost of the ticket. With a $1.4 billion jackpot, it’s easy money, right? Not so fast. Everyone knows that you don’t get the entire jackpot all at once. In order to get the cash payout, you give up approximately 38%, leaving you with $868 million (according to usamega.com). That’s a big haircut, but still well above the $586 million that you need for the expected value to be in your favor. Don’t forget about taxes! Nearly all of your winnings will be subject to the highest federal rate of 39.6%. After taxes, you’re taking home $524 million. Uh oh! That’s not enough!
After the cash payout option and federal taxes (not to mention state taxes), your expected value is only $1.79. But there’s more to this. The jackpot isn’t the only prize. You could come up short of the jackpot and still win a prize ranging from $3 all the way up to hundreds of thousands of dollars. And all of those non-jackpot prizes add to the expected value of the ticket. According to the folks at time.com, the expected value of the non-jackpot prizes is equal to $0.24. So, add that $0.24 to the earlier calculated expected value of $1.79 and now your $2.00 Powerball ticket has an expected value of $2.03. Winner, winner!
Unfortunately, it’s not that simple. Expected value calculations tell you the value of a wager over a large number of samples, not one ticket. In reality, your real-life expected value is $0. Yep, all that math, just to tell you that the expected value of your Powerball ticket is $0.Think of it this way. If you are watching a basketball game, and a player with an 80% free throw percentage steps to the line for two shots. Her “expected value” of those two free throws is 1.6 points. In reality, she can’t get 1.6 points. She’ll score 0, 1, or 2 points. This is the difference between mathematical probabilities and reality.
Taking this free throw analogy to an extreme. Let’s say another player’s free throw percentage is 0.00000034% (same as your Powerball jackpot odds), and he steps to the free throw line. But in this fictitious basketball game, he gets one free throw, and that free throw is worth 524,000,000 points. If he hits that free throw, your team wins HUGE! But what do you expect to happen? Let’s be honest, he’s going to miss.
This takes us right back to where we started. The lottery is a tax on people who are bad at math. Nearly every financial advisor (or math professor) will tell you that you shouldn’t play the lottery. I’m not one of them.
Back in the early-90s, I worked part time as a bank teller. One day, when the lottery reached the astounding jackpot of $100 million, everyone at my branch decided to put together a pool. We each pitched in our dollar, and one of the other tellers went out during her lunch break to buy the tickets.We spent the rest of that afternoon sharing our stories of what we would do with the money, or more accurately, how it would change what we would do with our lives. I heard stories of returning to school, dream vacations, dream homes, dream businesses, dreams for their families. Dreams. For a day and for a dollar, a bunch of bank tellers, new accounts officers, and assistant bank managers shared their dreams with each other.I learned more about my co-workers on that one day than the rest of the three years or so that I worked with them.
So, go ahead and play the Powerball. Do it in moderation, and give yourself license to dream. Share those dreams with friends, co-workers, and loved ones. Learn about their dreams. On Wednesday, when they draw numbers that are different from the ones on your ticket, don’t forget those dreams.