If the human mind is susceptible to change, whats the use of strong convictions?

Convictions help you make the right choice when you are in a tough situation or you are feeling tempted. I don't understand your reasoning - because the mind *might* change, there's no use in having strong convictions, so why even bother, why not just let yourself get tossed around like a piece of flotsam with every wave that washes by? I don't get it.