This research paper analyses three strategy games—Chess, Othello, and Poker—from the perspective of game theory. Mathematical modeling techniques are used to develop optimal strategies for each game to provide insights into their underlying principles and dynamics. The analysis reveals many similarities between the two-player abstract board game Chess and its modern variant Othello. It also highlights substantial differences compared to probability models explicitly developed for Poker. The comparative examination provides an understanding of how different elements contribute towards developing successful gaming behavior across various contexts, which can be valuable information for strategic thinking and making informed decisions while playing such games or conducting similar activities like sports betting or investing in stock markets. Furthermore, implications drawn from this study suggest potential directions for further development within the field, including enhanced mathematical modeling methodology and improvement upon players’ decision-processing functionality, particularly during real-time play scenarios.
Game theory is a branch of mathematics concerned with studying participant interactions in situations where outcomes depend on multiple individuals’ collective choices (Colman, 2016).). It involves analyzing competitive scenarios involving two or more opponents with conflicting interests and determining strategic behavior based on predefined rules and objectives. The game theory finds applications in real-life scenarios such as economic markets, political elections, and popular Hollywood movies. This research paper explores the application of game theory in strategy games, with a primary focus on three variants: Chess, Othello, and Poker.
The analysis presented here adopts a mathematical modeling technique extensively used to develop optimal strategies in various gaming contexts. The methodology includes insights from probability theory, aiming to understand players’ decision-making processes during gameplay and enhance AI systems’ implementation with better accuracy levels in artificial intelligence topics. Additionally, the examination provides comparison results from different modeling techniques applied to these three variations, facilitating the identification of similarities and differences that surface when combined with human behavior elements in the gameplay. The implications drawn from this research offer valuable information for strategic thinkers and real-life sports betting and stock investing applications. The focus lies in understanding the underlying principles influencing decisions in different gaming contexts.
Over the years, researchers have conducted numerous studies on applying game theory to understand strategic behavior (Manshaei et al., 2013). These investigations have revealed patterns that govern players’ decision-making processes, influenced by their preferences, beliefs, and incentives at each level of play. Mathematical modeling techniques have been employed in these examinations, ranging from basic Decision Tree models to more complex Quantitative Game Theory approaches involving Integer Programming and Nash equilibrium values (Abedian et al., 2022). These techniques aim to develop tactical strategies that maximize rewards while minimizing risks within given constraints, providing valuable insights for research in this field.
This paper primarily focuses on three main areas: mathematics, computing science, and artificial intelligence systems. Mathematicians play a crucial role in interpreting and simulating games to reflect human behavior in real-life scenarios during gameplay accurately (Hamada & Sato, 2012). On the other hand, computer scientists contribute primary inputs in creating AI algorithms that efficiently detect patterns within datasets and implement strategies for survival and prediction of opponents’ potential moves based on probabilities and outcomes.
Regarding Chess, commonly employed mathematical models include the Minimax Decision Trees approach, which presumes perfect knowledge of opponents’ strategies (Saini, 2014). However, such assumptions only sometimes hold, as even expert-level gamers sometimes make strategic mistakes, leading to the development of advanced modeling approaches that involve probability theory and random variables to predict the chances of certain moves occurring. Probability Theory is applied to the variant of Othello, involving random elements that help players make tactical decisions with greater control over the game (Primanita et al., 2020). This approach also aids in identifying winning conditions more efficiently based on specific contexts experienced players have faced in the past due
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