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Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits…
Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
I postulate that human or other intelligent agents function or should function as follows. They store all sensory observations as they come - the data is holy. At any time, given some agent's current coding capabilities, part of the data is…
Current chess rating systems update ratings incrementally and may not always accurately reflect a player's true strength at all times, especially for rapidly improving players or very rusty players. To overcome this, we explore a method to…
Since its conception, the computer has found applications to accompany human creativity. Today, the debate about computers and creativity involves several challenges, such as understanding human creativity, modeling the creative process,…
Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…
Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects,…
Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…
In this paper, we will study the simplest kind of beauty that can be found in a simple piece of music and can be appreciated universally. The proposed approach shows that aesthetically appealing patterns deliver higher amount of information…
Providing consistent summative assessment to students is important, as the grades they are awarded affect their progression through university and future career prospects. While small cohorts are typically assessed by a single assessor,…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
In intuitive physics the process of stacking cubes has become a paradigmatic, canonical task. Even though it gets employed in various shades and complexities, the very fundamental setting with two cubes has not been thoroughly investigated.…
Chess and chance are seemingly strange bedfellows. Luck and/or randomness have no apparent role in move selection when the game is played at the highest levels. However, when competition is at the ultimate level, that of the World Chess…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
Algorithmic decision-making systems are increasingly used throughout the public and private sectors to make important decisions or assist humans in making these decisions with real social consequences. While there has been substantial…
Many circumstances of practical importance have performance or success metrics which exist implicitly---in the eye of the beholder, so to speak. Tuning aspects of such problems requires working without defined metrics and only considering…
We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each…
We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth…