Jack is designing a game for the school fundraiser. Players will be paying $$5$ for each time they play the game. There will be three prizes. The smallest prize has a value of $$5.50$; the next prize has a value of $$8$. Jack has not yet determined the value of the largest prize. The probability of winning the smallest prize is $0.15$, the probability of winning the second prize is $0.05$, and the probability of winning the largest prize is $0.01$. The probability of not winning any prize is $0.79$. If the school wants earn an expected value of $$1$ per game played, what should Jack choose as the value of the largest prize?