
arXiv: 2306.16079
We consider a card guessing game with complete feedback. A ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Then, the goal of the game is to maximize the number of correct guesses of the cards, where one after another a single card is drawn from the top, and shown to the guesser until no cards remain. Improving earlier results, we provide a limit law for the number of correct guesses. As a byproduct, we relate the number of correct guesses in this card guessing game to the number of correct guesses under a two-color card guessing game with complete feedback. Using this connection to two-color card guessing, we can also show a limiting distribution result for the first occurrence of a pure luck guess.
Combinatorial probability, Probability (math.PR), 05A15, 05A16, 60F05, 60C05, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Central limit and other weak theorems, Combinatorics (math.CO), Asymptotic enumeration, Game theory, Mathematics - Probability
Combinatorial probability, Probability (math.PR), 05A15, 05A16, 60F05, 60C05, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Central limit and other weak theorems, Combinatorics (math.CO), Asymptotic enumeration, Game theory, Mathematics - Probability
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