{"ID":2877856,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10471","arxiv_id":"2509.10471","title":"Bluffing in Scrabble","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.10471","url_pdf":"https://arxiv.org/pdf/2509.10471v1","authors":"[\"Nick Ballard\",\"Timothy Y. Chow\"]","published":"2025-08-26T02:20:32Z","proceeding":"math.HO","tasks":"[\"math.HO\",\"cs.GT\",\"math.CO\"]","methods":"[]","has_code":false}