Hold'em Probability Puzzler

[Carl_William]

Dear Huh,
You wrote:

"How many two-card hands, on average, will it take for you to see every card in a standard deck? I'll post my answer in a couple of days in a separate post. I'm curious to see how people get there.

Huh? "

I appreciate the challenge -- maybe I can solve it. Anyway -- I enjoy thinking about things like this -- maybe an excellent clue would be to solve it for a very small deck -- say 2 cards (too simple), 3 cards, 4 cards (etc.) and then proceed to 52 cards. Thanks again for the excellent post.

Most warm regards,
Carl William

PS: one could do a Bernoulli trial (binomial random variable) and determine the probability that 2 specific cards will or will not be dealt. But I think this is a counting technique problem not unlike the birthday classroom problem where the probability is determined (on average) that two or more people in a class were born on the same birthdate (i.e., month and day of month).