Abstract. Even after giving a standard 52-card deck a good shuffle, there will likely be instances where two cards with the same number end up next to each other. This article concerns my investigations into the probability of such an occurrence. In the end I found that this is by no means an uncommon event, there being a 21.7% probability of finding two cards of a given number adjacent, and a 95.4% chance of finding at least one pair of adjacent same-numbered cards. I made these calculations using combinatorics for up to 20 cards, and a random number-based simulation for the cases of 24 to 52 cards.

Received: January 17, 2013

AMS Subject Classification: 60C05, 97K50, 00A08

Key Words and Phrases: probability, combinatorics, counting, complimentary events, random numbers, simulation

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