Hi all!

I'm working on a project where I'm wanting to find exact probabilities for events in regards to a shuffled deck of cards.  

As the number of possible shuffles is so high, an analysis of a sample doesn't seem to be nearly accurate enough.  This seems like a simple task, but I just can't get my head around it!!

So the question is this; if I were to shuffle a deck of cards properly, and then lay the cards out in the order in which they've been shuffled, what is the probability that two sequential cards would form a "pair"?  What are the chances of two "pairs" appearing anywhere in the shuffle?

Thanks in advance!