What is your expected value for a game where your probability of winning is 1/9 and your profit is four times your wager?

Suppose you wager x amount. There are two possibilities: winning 4x (probability 1/9), or losing x (probability 8/9). The expected value for your winnings is thus:
8/9 * (-x) + (1/9) * (4x) = -4/9 x.