Related papers: A Multi-Computational Exploration of Some Games of…
In a delightful article that recently appeared in Mathematics Magazine, David and Lori Mccune analyze the board game "Count Your Chickens!", recommended to children three and up. Alas, they use the advanced theory of Markov chains, that…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Many popular video games use pseudorandom number generators to create randomly distributed locations for game objects as highly unpredictable as possible. Some scenarios like game competition also need reproducible randomness, namely the…
The power of symbolic computation, as opposed to mere numerical computation, is illustrated with efficient algorithms for studying the generalized gambler's ruin problem in one and two dimensions. We also consider a new generalization of…
Learning to code, and more broadly, learning about computer science is a growing field of activity and research. Under the label of computational thinking, computational concepts are increasingly used as cognitive tools in many subject…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
The game of Gyan Chauper or snakes and ladders exists in many forms throughout history as a board game of varying size, structure, and game elements of snakes and ladders associated with various vices and virtues inscribed within the board.…
People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…
Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…
Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler…
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…
This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains,…
Games have long been a microcosm for studying planning and reasoning in both natural and artificial intelligence, especially with a focus on expert-level or even super-human play. But real life also pushes human intelligence along a…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation -- that is, computation of successive bits of information upon request. The core of the approach surveyed here dates back…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…