Applying the Hypergeometric Distribution to Yu-Gi-Oh! TCG Deck Planning

Abstract

This paper investigates an application of the hypergeometric distribution in the Yu-Gi-Oh! TCG context, from a competitive and probabilistic perspective. The construction of a main deck has always been a critical factor to guarantee consistent wins in Yu-Gi-Oh! TCG, and many players employ strategies that implicitly rely on an empirical insight of probability, including the hypergeometric distribution inherent in their deck. This probabilistic insight is used to maximize the probability of obtaining an advantageous opening hand. The main objective of this paper is to show how Yu-Gi-Oh! TCG players, especially in the context of large-scale tournaments, such as the Yu-Gi-Oh! Championship Series (YCS), can use the hypergeometric distribution to optimize the performance of their decks. The model proposes 6 combinations, with 5 cards each, that result in an advantageous opening hand, based on a specific categorization of cards. From the perspective of the competitive Yu-Gi-Oh! TCG scenario, this paper helps beginner players build their decks and assists experienced players in confirming the ideal proportions to achieve different advantageous card combinations on the first turn. Furthermore, it shows a set of useful information for players, organized in tables.