Guessing Strategies for Shuffling Machines (2507.10294v1)

Published 14 Jul 2025 in math.PR and math.CO

Abstract: We investigate a one-time single shelf shuffle by establishing the position matrix explicitly. In some cases, we prove a no-feedback optimal guessing strategy. A general no-feedback strategy is conjectured, and asymptotics for the expected reward are given. For the complete-feedback case, we give a guessing strategy, prove that it is optimal and unique, and find the expected reward. Our results prove a conjecture of Diaconis, Fulman, and Holmes in a special case.

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Authors (1)

Alexander Clay

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