Guessing Strategies for Shuffling Machines
Probability
2025-07-15 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2507.10294,
title = {Guessing Strategies for Shuffling Machines},
author = {Alexander Clay},
journal= {arXiv preprint arXiv:2507.10294},
year = {2025}
}