Optimal Decision Strategies for the Generalized <i>Cuckoo</i> Card Game

Cuckoo is a popular card game, which originated in France during the 15th century and then spread throughout Europe, where it currently well-known under distinct names with different variants. Cuckoo an imperfect information game-of-chance, makes research regarding its optimal strategies determination interesting. The rules are simple: each player receives covered from dealer; starting at dealer's left, looks own decides whether to exchange their or keep it; dealer plays last and, if card, draws random one remaining deck; player(s) lowest valued lose(s) round. We formulate gameplay mathematically provide analysis of decision policies. Different decks can be used for this e.g., standard 52-card deck Italian 40-card deck. generalize model arbitrary number decks' cards, suites, players. Lastly, through numerical simulations, we compare determined strategy against benchmarks, showing that outperforms naive policies approaches performance ideal oracle.