A friend of yours offer to play with you the three games below that involve rolling a single $6-$sided die: Game $1$: You pay $3$ cents and win in the cent amount on the roll Game $2$: You pay $1$ cent and win $2$ cents if the roll is odd. Game $3$: You pay $2$ cents and win $8$ cents if the roll is at least a $5.$ Which game is the best in terms of expected payoff, and which game is the worst? Explain your reasoning or show your work.