Snap by Rank
Two standard 52-card decks are shuffled independently and uniformly at random. Their cards are turned over in pairs, one from each deck, for 52 turns. A turn is a match if the two cards have the same rank (suits are ignored). What is the probability that none of the 52 turns is a match? Give your answer as a decimal rounded to four places.
Related problems & prerequisites
Worth solving first
- A Hand with a Void 6.0/10
- A Boy Born on Tuesday 6.0/10
Source: Generalisation of Montmort's problème des rencontres to repeated ranks, treated via rook polynomials in Riordan, An Introduction to Combinatorial Analysis. Statement written for AxiomIQ.