Question

Average no. of cards in two decks which will match

Answer 1

Completely shuffle and then lay out a full deck of 52 cards in a single row (i.e. single row 52 columns). Do the same thing with a second deck of playing cards and place this deck in the second row(also has 52 columns). What is the expected total number of matches in all the columns?

A match means that the top card and the bottom card in the column are the same (same rank and suit).

I was trying to solve it by brute force but seems like it's not that easy to me.