So in the simplest sense the jackpot times your odds of winning should be larger than your wager
So if there are 200 tickets sold for a dollar and one winner will be drawn you could figure your break even point as
Jackpot * (Your Tickets / Total Tickets) = Your Wager
J * (1 / 200) = 1
The only thing you’re adding with a real world lotto is the fact that more than one can win because you’re not concerned about your chances of not winning (and the pool continuing) only your chances of winning and having to split the pot (which reduces your expected gain).
I’m guessing the best you could do without analyzing the numbers people tend to play is assume an even distribution and try to figure the number of probable winners that way.
So you’d have to correct your expected winnings for the number of probable winners. This gets fuzzy because you won’t have a partial winner, but I believe for figuring your odds, a partial winner would be fine.
So you’d be looking at
Probable Winners = Total Tickets / Possible Scenarios (a specific set of numbers)
(Jackpot / Probable Winners) * Odds = Cost
So if your scenario is 200 tickets, sold for a dollar, numbered from 1 to 100, and all money is awarded your equation would be
(200/2) * 1/100 = 1
That figures your break even point, so really you’d want the left side to be larger than the right.
To fill in some blanks with the mega million jackpot
Jackpot was 640,000,000
Odds are 1 in 175,711,536
Jackpot before the big one was $363 million, so we can assume at least 300 million tickets
Tickets are $1
So we’re looking at
Probably winners = ~300,000,000/175,711,536 – make this 2 for ease
(640,000,000/2) * (1/175,711,536) = 1.82
Which is bigger than the $1 cost of a ticket and doesn’t figure in smaller prizes.