Bluffing in Scrabble
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918140352397312 |
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| author | Ballard, Nick Chow, Timothy Y. |
| author_facet | Ballard, Nick Chow, Timothy Y. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bluffing in Scrabble Ballard, Nick Chow, Timothy Y. History and Overview Computer Science and Game Theory Combinatorics 91A05 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. |
| title | Bluffing in Scrabble |
| topic | History and Overview Computer Science and Game Theory Combinatorics 91A05 |
| url | https://arxiv.org/abs/2509.10471 |