Take two standard decks of 52 cards and shuffle them together. Now deal the cards out in a single row. How would you compute the probability that somewhere in that row of 104 cards there are two matching cards next to each other? Where “matching” means the same suit and rank. Not the probability of a specific card (e.g. the two of clubs) being next to it’s mate from the other deck, but of any two “mates” being next to each other.
My intuition tells me that it’s probably fairly likely that in any random shuffle, there will be at least one matching pair SOMEWHERE in there, but I don’t know how to go about computing the probability.