Help, I have no idea what to do! Many lottery games for very large prizes include guessing which numbers will appear from a random sample of the numbered balls. In Minnesota's Gopher 5 lottery, there are five balls numbered 1-47. If a player matches at least two balls, she wins a prize (see table below).

If the cost of playing is $1, at least how large must the jackpot be before the expected return of playing Gopher 5 becomes favorable to the player? Assume there is only one winner, and also ignore the fact that winnings are also taxed.

Match Win Odds
5 of 5 Jackpot 1 in 1,533,939
4 of 5 $500 1 in 7,304
3 of 5 $15 1 in 178
2 of 5 $1 1 in 13