Friday night’s Mega Millions draw increased to an estimated $ 1 billion jackpot, which marks the third largest lottery jackpot in history.
But does that mean that now is the best time to join other people when buying a ticket? Here’s what the math says.
Players and mathematicians look for ‘expected value’
Historical lottery data reveals that buying a lottery ticket when the jackpot is at a record high is not necessarily the smartest move, in part due to an often overlooked factor: the chances of having to split the jackpot. But what about third largest jackpot?
When the jackpot reaches a notable size, ticket sales tend to increase exponentially – a phenomenon well documented by computer scientist Jeremy Elson. As more and more people buy tickets, the likelihood of seeing the jackpot split between multiple winners also increases. And that can have a big impact on the overall expected value of any lottery ticket.
When players and statisticians evaluate whether a bet is worth it or not, they look at what is called the expected value. In a single bet, it is usually calculated by multiplying the probability of winning a bet by the payout. For example, the expected value of a $ 1 payout on a heads or tails would be calculated as 0.50 times $ 1, or 50 cents.
Therefore, a rational player would be willing to bet up to 50 cents for a bet with these parameters. Throwing more than 50 cents would be a lost proposition over time.
Of course, when it comes to the lottery, the chances of winning are much worse than heads or tails. The probability of winning a Powerball jackpot is approximately 1 in 292 million, compared to about 1 in 303 million for Mega Millions. This probability is constant, no matter how many tickets are sold, as well as the adjustments that need to be made to account for taxes and convert the advertised annuity jackpot into a fixed dollar amount.
But the fact that the probability of splitting a jackpot depends on how many tickets are sold means that the expected value of a lottery ticket tends to decrease as the jackpots approach record values.
In fact, according to Elson, the expected value of lottery tickets tends to increase when jackpots reach large amounts – but not so large that they become “mandatory” events. For Friday’s draw, assuming 150 million Mega Millions tickets sold, there is about a 30% chance of a single person winning the jackpot, and about an 8% chance of seeing two or more winners. In the record Mega Millions jackpot in 2018, which saw more than 370 million tickets sold, the chances of two or more winners were 23%.
That said, people generally don’t buy a lottery ticket based on expected values, since the $ 2 cost of an individual lottery ticket is theoretically always higher than the expected value (the house always wins). But that begs the question: why, then, are millions of people buying tickets?
Behavioral economists often echo the established work of researchers Daniel Kahneman and Amos Tversky, who originally pointed out that humans have a tendency to overestimate low probability events, such as about 1 in 303 million chances of winning a lottery prize.
Zack Guzman is an anchor of Yahoo Finance Live and also a senior writer who covers entrepreneurship, cannabis, startups and breaking news on Yahoo Finance. Follow him on Twitter @zGuz.
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