Two Spins Against One

A carnival booth runs this game. You spin a fair six-sided spinner **twice** and keep your better result. The house spins the same spinner **once**. You win if your kept number is strictly greater than the house's; if the two are equal the game is a push and your stake is returned; otherwise you lose your stake.

(a) What is your probability of winning?

(b) At even money on a $\$1$ stake, what is your expected profit per play?