Let's suppose I have n playing cards and I need to find k specific ones by going through them one by one. It does not matter what order I find the cards in, but any of the k cards could be anywhere in the deck. What is the average number of cards, that would I be expected to discard before finding the very first card I wanted? I can see the trivial cases where if I knew that all of the cards that I needed were together at the bottom of the deck, I would have to discard n-k, and if just the first card I needed were at the top, I would discard 0 before getting to it. However, I can't generally assume that I know where the cards are going to be, so these special cases aren't particularly helpful except as examples of the upper and lower bounds. It seems to me that if k were 1, then the average number of cards to skip would be n/2, but I don't know how to calculate for a general k where n $\ge$ k $\ge$ 0.
I know how to calculate the number of total possibilities in n choose k, but I can't figure out how to tell what the average number of skipped entries would be for finding just the first one.