There are 6 possibilities for rolling doubles, corresponding to rolling (1, 1), (2, 2), ..., (6, 6). There are 2 possibilities for rolling a sum of 3: (1, 2) or (2, 1). Note that the event of rolling a 3 and the event of rolling doubles are mutually exclusive, meaning that both cannot happen at the same time. Therefore, to find the probability of rolling a 3 or doubles, we just add the probabilities of the two events: $$ \text {P} (\text{rolling a 3 or doubles}) = \text{P} (\text{rolling a 3}) + \text{P} (\text{rolling doubles}). $$Since there are 36 possible outcomes in total, we find that $$ \text{P} (\text{rolling a 3}) = \frac{2}{36} = \frac{1}{18} \quad \text{and} \quad \text{P} (\text{rolling doubles}) = \frac{6}{36} = \frac{1}{6}, $$and the requested probability is $$ \frac{1}{18} + \frac{1}{6} = \frac{1 + 3}{18} = \boxed{\frac{1}{6}}. $$
