Bluffing in Scrabble

[2509.10471] Bluffing in Scrabble Skip to main content Search Submit Donate Log in Mathematics > History and Overview arXiv:2509.10471 (math) [Submitted on 26 Aug 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Bluffing in Scrabble Authors: Nick Ballard , Timothy Y. Chow View PDF HTML (experimental) Abstract: It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the optimal strategy involves bluffing, or even a Scrabble position in which the optimal strategy is a mixed (i.e., randomized) strategy. We present a carefully constructed Scrabble position, that could actually arise in a tournament game with no invalid words played, in which the optimal strategy (assuming that a tied score leads to the point being split equally, with no recourse to so-called "spread points" as a tie-breaking mechanism) is to make Move A with probability 1/3 and to make Move B with probability 2/3. Move B can reasonably be called a bluff, in the sense that it sets up a threat which the player cannot in fact execute, but which the opponent may not be able to rule out. Comments: 17 pages Subjects: History and Overview (math.HO) ; Computer Science and Game Theory (cs.GT); Combinatorics (math.CO) MSC classes: 91A05 Cite as: arXiv:2509.10471 [math.HO] (or arXiv:2509.10471v2 [math.HO] for this version) https://doi.org/10.48550/arXiv.2509.10471 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Timothy Y. Chow [ view email ] [v1] Tue, 26 Aug 2025 02:20:32 UTC (866 KB) [v2] Thu, 27 Aug 2026 04:07:33 UTC (867 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.HO < prev | next > new | recent | 2025-09 Change to browse by: cs cs.GT math math.CO References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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