Originally Posted by

**romsek** The answer is a bit counter intuitive at first but on reflection becomes clear.

The answer is that the probability of selecting your joker after k draws is $\frac{1}{53}~\forall k \in 1,2,\dots 53$

Think about it this way. Is the joker any different from any other individual card? No. Thus it's just as likely to find any selected card at the kth draw as it is to find the joker. If all the cards have equal probabilities then they must all have probability $\frac{1}{53}$ at each draw.

The sum of all these probabilities is just $53 \cdot \frac{1}{53}=1$