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math.PR2026
Optimal complete-feedback card guessing under nonincreasing valley weights: A proof of the Diaconis-Fulman-Holmes shelf-shuffling conjecture
Congyi Luo
Let a random permutation represent the order of distinct cards. After each guess, the player learns the actual card, and the objective is to maximize the expected to…
math.PR2026
Extremal expectations in card guessing with partial feedback: proofs of two conjectures of Diaconis-Graham-Spiro
Congyi Luo
We study the minimum and maximum expected scores over all adaptive strategies in sequential card guessing with yes/no feedback. A deck contains labels, each appearing times…