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At $2B, is it worth it to play Powerball?
Market Mysteries of the week
Is it worth it to play Powerball?
Answer:
Last week, someone in California won $2 billion playing Powerball, the largest lottery prize the world has ever seen. As the pot size increases, that $2 ticket gets more valuable, but deciding whether it's worth the cost depends on your risk appetite.
How does Powerball work?
Anyone with $2 can win more money than they can imagine.
To win the
jackpot, you need to match five lottery numbers — white balls numbered from 1-69 — plus the red Powerball, numbered from 1-26. Each Powerball ticket costs $2, and for an extra $1, you can activate the Power Play, increasing your payout for non-jackpot prizes. By matching a partial ticket, you can still win up to $1 million or $2 million with a Power Play.
If no one wins the jackpot, the pot size rolls over to the next drawing, increasing as more people buy tickets.
The longer without a winner, the bigger the jackpot grows. Last week's $2 billion pot was the result of a
While the odds of winning a prize in Powerball ($4 or more) are decent,
,
the odds of winning the Powerball jackpot are incredibly slim
: 1 in 292,201,338. You have to pick at least four balls correctly to win $100 or more, which is a 1 in 14,494 probability.
Is Powerball ever worth playing?
It depends on how you value chance.
Would you rather have $1 in your pocket or a 1-in-10 chance at $10? What if it's $10,000 or a 1-in-10 chance at $100,000? If you were a math team kid like us, you might be a fan of a metric called expected value (probability-weighted winnings). The value of the ticket is different than what you pay for it.
As the potential reward increases, your ticket gets more valuable.
So if the probability-weighted value of the ticket is greater than its cost, the ticket might be
worth it
.
First off, the expected value from the non-jackpot prizes stays the same.
You always have the same chance of winning $4, $7, $100, $50K, or $1M. We can estimate that
. That's far from the $2 cost of the ticket. If you pay an extra dollar for the Power Pay prize multiplier, the ticket's expected value goes up to $0.81. So by paying 50% more, your expected value increases by 2.5x. Again, it's still far from covering its own cost, but then you have to identify the value from the jackpot.
As the jackpot size increases, buying a ticket gets more worth it.
So, can the jackpot get big enough that the probability-weighted value exceeds that extra $1.68? If we have a 1-in-292M chance at winning, then a $292M pot means the expected value would be $1. So you might say a $490M jackpot adds $1.68 of expected value, making the ticket worth $2. So does a $500M jackpot make it worth it? Not so fast.
Two significant considerations eat away at your expected return: taxes and other people.
First off, Uncle Sam will take nearly half of the prize money. So even if you won the jackpot, your take-home cash is far lower. Beyond that, Powerball can have multiple winners. So as the pot increases, more people buy tickets, and the chance of taking home the entire pot as a single player decreases and eats into your probability-weighted reward.
When considering taxes and players,
a ticket's mathematical maximum expected value peaks at about $0.85 when the jackpot reaches about $500M.
After that, the estimated value decreases as more people join the game.
So the ticket will never be mathematically "worth it,"
but probabilities are only that. The California winner of the $2B did not have to split with any other players. That extra $1.15 of pure risk was worth it for them.
So should I play in the next Powerball?
Buying the occasional $2 is totally up to you, but
it's likely only worth it to play in occasional big jackpots, especially if you don't have a lot of spare income.
Some consider the lottery to be a
. Inadequate financial education in schools and inaccessible financial services have put investing out of reach for many Americans, forcing many to turn to the lottery as their primary opportunity for betterment.
than wealthier individuals on lottery tickets, both in absolute value and relative to their income.
There are likely better things to do with your money each week,
especially with easier access to low-cost investing. Instead of spending $6/week on lottery tickets for the last 20 years, if you invested that money in the stock market with a broad total market fund, you could have $20,000 right now. It's not $2 billion, but it's better than spending six thousand dollars on nothing. That said, we all know investing isn't a guarantee either. It's about making the best risk-adjusted decisions with your dollars.
Will you be buying a ticket for the next big jackpot?
âš¡The Share Scoops Team
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