Related papers: Modelling Chess in VDM++
In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit…
Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this AMS Notices article, we focus on the decision-making development for the intervention of…
The limit of a sequence by the definition with $\varepsilon$ is introduced by the notion of checkmate in two moves. The idea is also extended to define the limit of a function with $\varepsilon$ and $\delta$.
In the "Game about Squares" the task is to push unit squares on an integer lattice onto corresponding dots. A square can only be moved into one given direction. When a square is pushed onto a lattice point with an arrow the direction of the…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
Context-free games are two-player rewriting games that are played on nested strings representing XML documents with embedded function symbols. These games were introduced to model rewriting processes for intensional documents in the Active…
This report documents the development, test, and application of Large Language Models (LLMs) for automated text analysis, with a specific focus on gambling-like elements in digital games, such as lootboxes. The project aimed not only to…
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…
Human societies engage in a number of games which use tokens as a means to allocate, issue and access gated resources and property rights: The notion of exchanging tokens that represent and carry value from the past into the future to…
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…
Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What…
We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…
This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they…
A 5x5 board is the smallest board on which one can set up all kind of chess pieces as a start position. We consider Gardner's minichess variant in which all pieces are set as in a standard chessboard (from Rook to King). This game has…
In this paper, we show that investigating the interaction of conversational type (often known as language game or speech genre) with the character types of the interlocutors is worthwhile. We present a method of calculating the decision…
We consider a two player simultaneous-move game where the two players each select any permissible $n$-sided die for a fixed integer $n$. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for $n>3$,…
[Spreadsheet] Models are invaluable tools for strategic planning. Models help key decision makers develop a shared conceptual understanding of complex decisions, identify sensitivity factors and test management scenarios. Different…
This paper examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…