Related papers: Statistical mechanics for Scrabble predicts strate…
We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial (and arbitrary), we…
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…
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
This paper explores the entertainment experience and learning experience in Scrabble. It proposes a new measure from the educational point of view, which we call learning coefficient, based on the balance between the learner's skill and the…
We study sequential language games in which two players, each with private information, communicate to achieve a common goal. In such games, a successful player must (i) infer the partner's private information from the partner's messages,…
With the rising popularity of Wordle, people have eagerly taken to Twitter to report their results daily by the tens of thousands. In this paper, we develop a comprehensive model which uses this data to predict Wordle player performance and…
The scramble number of a graph is an invariant recently developed to study chip-firing games and divisorial gonality. In this paper we introduce the screewidth of a graph, based on a variation of the existing literature on tree-cut…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…
The current state-of-the-art Scrabble agents are not learning-based but depend on truncated Monte Carlo simulations and the quality of such agents is contingent upon the time available for running the simulations. This thesis takes steps…
In this paper, I apply linguistic methods of analysis to non-linguistic data, chess plays, metaphorically equating one with the other and seeking analogies. Chess game notations are also a kind of text, and one can consider the records of…
A game-theoretic model of scrip (artificial currency) systems is analyzed. It is shown that relative entropy can be used to characterize the distribution of agent wealth when all agents use threshold strategies---that is, they volunteer to…
This work investigates the role of uncertainty in Slay the Spire using an information-theoretic framework. Focusing on the entropy of game paths (which are based on procedurally-generated maps) we analyze how randomness influences player…
In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of a graph, was recently developed as a tool for lower…
Construction grammar posits that constructions, or form-meaning pairings, are acquired through experience with language (the distributional learning hypothesis). But how much information about constructions does this distribution actually…
Wordle is a very popular word game that is owned by the New York Times. We can design parameterized strategies for solving Wordle, based on probabilistic, statistical, and information-theoretical information about the games. The strategies…
Games are often designed to shape player behavior in a desired way; however, it can be unclear how design decisions affect the space of behaviors in a game. Designers usually explore this space through human playtesting, which can be…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…