Guessing about Guessing: Practical Strategies for Card Guessing with Feedback. Issue 7 (9th August 2022)

• Record Type: Journal Article
• Authors: Diaconis, Persi; Graham, Ron; Spiro, Sam
• Is Part Of: American Mathematical Monthly. Volume 129:Issue 7(2022)
• Page Start: 607
• Page End: 622
• Publication Date: 2022-08-09
• Subjects: Primary 60C05; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2022.2069986
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g., correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where suits do not matter), the optimal strategy differs from the "greedy strategy" (of guessing a most likely card each round). Further, both optimal and greedy strategies are far too complicated for real-time use by human players. Our main results show that simple heuristics perform close to optimal.