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The Odds on Lottery Tickets


The Odds on Lottery Tickets

For all who dream of winning big and reaping rewards, Jacob Lehman delivers the best odds in probability to help you to decide which ticket to buy.  

NOTE: The following post discusses the New York and multistate lotteries as an exercise in probability and decision-making. It does not constitute financial advice or recommendations. You must be 18 years or older to purchase a lottery ticket. If you are struggling with a gambling addiction, please call the HOPEline 1-877-8-HOPENY (1-877-846-7369) or text HOPENY (467369)

I’m fascinated by how we think about risks and rewards in various contexts, especially when the rush to get to AN answer gets in the way of thinking a problem through to its conclusion. The lottery provides an object lesson in this type of reasoning. There are two major jackpot games in the US, Mega Millions and Powerball. As I write this, the Mega Millions jackpot drawing for tomorrow has a top prize of $600 Million, while the Powerball has a top prize of $550 million.*

Suppose I have a bit of a gambling streak, and ask for your advice on how to buy a bunch of lottery tickets. I might as well go for the Mega Millions, since it has a 10% higher payout, right?

Not so fast, you say. I’m smart and took stats in high school, let me compare the odds of those jackpots. The Powerball odds are 1 in 292 Million, while the Mega Millions jackpot is 1 in 302.5 Million. Okay, that yields an expected value of $1.88 for the Powerball per $2 play, and only $1.98 for the Mega Millions. So our gap is down to around 5%, but still argues in favor of the Mega Millions.

Ah, but that’s not the only prize. Even if we don’t win the jackpot, we might at least recoup our costs with some smaller prizes (and maybe even come out ahead). Let’s compare those, first for the Powerball:

2nd Prize is $1,000,000 with a probability of winning of 1/11,688,053, yielding an expected value of $0.09. Continuing that logic with the lower prizes yields an additional $0.24, for a Total Non-Jackpot EV of $ 0.33.

Performing the same calculations on the Mega Millions gives us a Total Non-Jackpot EV of $ 0.25.

Okay, now we’re getting somewhere interesting! So the Mega Millions Expected Payout (with Jackpot) is $ 2.23, while the Powerball expected Payout (with Jackpot) is only $2.21. So even closer, but still argues for the Mega Millions. And, since the payout is higher than the $2 cost of a ticket, should you put all of your assets into lottery tickets?


Key points include:

  • The Powerball odds
  • The Mega Millions jackpot
  • The data on best chances 


Read the full post, How to Win the Lottery: Risks, Rewards, and Decision-Making, on LinkedIn.