#### Do the math ...

OK ...

I googled Mega Millions, it seems there are 5 numbers between 1 & 75, and 1 number between 1 & 15. The chances of getting all six is therefore one in 15 * 75! / ( (75-5)! * 5!) which is about 1 in 259 million (258,890,850)

The probability that you won't win is therefore (258,890,849 / 258,890,850 ) per play or about 0.99999999613. The probability that nobody will win in a draw with N plays is this number to the power of N. Where N is a million, that is 99.6%, but where N is a billion it is only 2%, so it doesn't seem that unlikely. Interestingly, that's nearly the exact opposite of your guess --- if 1 billion plays were made then the jackpot would get won 98% of the time!

If you want to work out what N is to so that the jackpot is won about 30% of the time, you need to work out what power you'd need to raise the non-win probability to to get 0.7 (i.e. a 70% chance no one wins a given draw). This is log (0.7) / log (258,890,849 / 258,890,850) which is about 92.3 million.

It doesn't seem at all unlikely to me that a 44 state lotto might get this many plays, it's probably only what, one play per average 2 head of population?

PS: didn't down vote you, because almost nobody can calculate probabilities like this intuitively, hence things like the birthday problem.