English

Matching adjacent cards

Combinatorics 2025-01-15 v1

Abstract

In a well-shuffled deck of cards, what is the probability that somewhere in the deck there are adjacent cards of the same rank? What is the average number of adjacent matches? What is the probability distribution for the number of matches? We answer these and related questions for both the standard 5252-card deck with four suits and 1313 ranks and for generalized decks with kk suits and nn ranks. We also determine the limiting distribution as nn goes to infinity with kk fixed.

Keywords

Cite

@article{arxiv.2501.07753,
  title  = {Matching adjacent cards},
  author = {Kent E. Morrison},
  journal= {arXiv preprint arXiv:2501.07753},
  year   = {2025}
}
R2 v1 2026-06-28T21:05:21.231Z