If A draws a smiling face, the probability of B winning the prize is1/3; If A draws a smiling face, the probability of B winning the prize is 2/3. Then the probability of B winning the prize is 1/3 or 2/3. In the case that A draws cards without looking at them, the probability of B winning is 1/2.

So the winning probabilities of A and B are both 1/2.