Then overlay this info with the hypothetical of buying every possible ticket, and this hypothetical buyer is almost guaranteed to split the pot. And that would drive the expected value of buying all possible tickets to a negative number.

Back of the envelope numbers:

300 million tickets at \$2 each is an outflow of \$600 million.

A headline jackpot of \$1.2 billion would give a single payment of perhaps 60% of that, let’s say \$700 million.

I recall someone else posting stats that showed, IIRC, with a headline jackpot like that, the odds of having no winner was about 7%. In our hypothetical, that becomes the odds of our buyer being the sole winner. 93% of the time, the pot would be split.

Keeping it simple with just one other winner, the EV of that 93% is 700 / 2 * .93 or \$325 million. The other partial EV is 600 * .07 or \$42 million. Add the two partials, and the total EV is \$367 million. Subtract off the initial investment and we’ve got something significantly negative.

—Peter

PS - There should probably be an adjustment for the effect on the jackpot of buying that many tickets. I’ll let someone else figure out what that might be.