One way to look at this is with the Kelly Criterion (https://en.wikipedia.org/wiki/Kelly_criterion), which says that in order to maximize the long-term growth rate of your capital, you must maximize the geometric mean of your capital at the end of each decision point. To make this concrete, I'll take CA Powerball as an example. According to http://www.calottery.com/play/draw-games/powerball/faqs , the jackpot starts at $40 milllion, and your odds of winning are 1 in 293 million. For simplicity I will neglect the other (smaller) prizes, and the chance of splitting the jackpot with someone else, taxes, time value of money, etc.

Suppose you have $100k in the bank, and tldroptions.io says you have a 20% chance of receiving a $60 million payout. The geometric mean of your capital is then $360k: https://www.wolframalpha.com/input/?i=exp%28.2+log%5B60%2B.1...

It would take 62 million CA powerball tickets (each with different numbers, in the same drawing) to give the same result: https://www.wolframalpha.com/input/?i=exp((x%2F293000000)*+l...