Is there ever an odds to payout ratio that makes purchasing a lottery ticket a mathematically rational choice?
I realize that you have to factor in multiple winners splitting the prize, the odds that will happen etc. Let’s have the most basic case, where you buy a ticket for $1 with 1 number between 1 and 10 and the winner gets $100 trillion. In such cases, the mathematician would buy as many of each number as he could possibly afford. Of course everyone else would be doing the same. Even still, I suspect that such a lottery would still net a nice return even split several billion ways.
So how would a rational mathematician calculate when the odds are actually in her favor to win, given that there could be many other winners?
This question is in the General Section. Responses must be helpful and on-topic.