*“Everybody else is playing the Mega Millions, so I figure my odds are better with the PowerBall.”*

*This would be funny, except, of course, I was standing in line to buy a Mega Millions ticket too, so I can’t really snark on someone for their lack of math skills.*

It would be an interesting exercise to figure at what lotto jackpot value the return on a ticket maximizes. It’s not nearly so simple as larger jackpot = more return because the number of people buying tickets, and the number of tickets bought per person buying tickets both spike when it gets really high, so the odds of having to split the jackpot go up as the jackpot does.

I spent a few minutes not too long ago to calculate the expected value (EV) of a ticket, ignoring that effect of split pots, and if I did them right, I found that the cash value of the jackpot (not the headline number, which is paid out over 20 years or something, but the cash out now number) has to hit about $500 million, which is ballpark $800 million headline value, IINM, before the EV turns positive. That still ignores the effects of taxes, but I figure I’d donate the vast bulk of it to charity the first year to avoid most taxes.

Any way, I went to looking for an estimate of what effect the pot-splitting has, and the news was not good. I can’t vouch for his calculations but it looks plausible, second answer down: https://www.quora.com/What-are-the-odds-of-having-multiple-w…

He said at the time, when the lotto was spiking over $1b, the last round had produced about 450 million ticket sales and he ran his estimates as if 600 million tickets were sold as it went over $1b. “Then we get that the probability of no tickets winning is 0.135, one winning 0.271, two winning also 0.271, three winning, 0.180, four winning 0.090, and five winning 0.036.”

So if you win in this scenario, you are most likely splitting the jackpot, and you’re more likely to split with more than one other ticket than you are to win it by yourself.

This obviously craters any potential positive EV in this scenario.