Authors
Persi Diaconis, Ron Graham, Xiaoyu He, Sam Spiro
Publication date
2022/1
Journal
Combinatorics, Probability and Computing
Volume
31
Issue
1
Pages
1-20
Publisher
Cambridge University Press
Description
Consider the following experiment: a deck with m copies of n different card types is randomly shuffled, and a guesser attempts to guess the cards sequentially as they are drawn. Each time a guess is made, some amount of ‘feedback’ is given. For example, one could tell the guesser the true identity of the card they just guessed (the complete feedback model) or they could be told nothing at all (the no feedback model). In this paper we explore a partial feedback model, where upon guessing a card, the guesser is only told whether or not their guess was correct. We show in this setting that, uniformly in n, at most cards can be guessed correctly in expectation. This resolves a question of Diaconis and Graham from 1981, where even the case was open.
Total citations
20212022202320243862
Scholar articles
P Diaconis, R Graham, X He, S Spiro - Combinatorics, Probability and Computing, 2022