A real-world Markov chain arising in recreational volleyball (Q2668137)

This work studies a Markov chain which describes how 24 players are mixed in 4 teams between several games in a recreational volley club. It combines two mechanisms: first, following standard volley rules, the players rotate within a team during a game, and second, some players change team between two games depending on their position. This bears some similarities with card shuffling models. The work is presented as a nontrivial pedagogical undergraduate project. Despite the relative simplicity of the chain, proving aperiodicity and irreducibility requires some combinatorial work. This study is followed by a more quantitative study of a simpler chain which describes the relative position between two given players (instead of the whole configuration of the 24 players).