Enhancing the Probability of Victor for Top Players via Knockout Tournament Fixture

A tournament fixture is an integral part of the tournament rules. It determines the random pairing of contestants, with several matches played per round. The selection of fixture type that optimizes the top player's winning probability significantly affects the financial aspects for organizers, individuals, and participants while also addressing the interests of millions of fans. In addressing this challenge, this study designed a balanced tournament fixture and employed a labeling system to represent each fixture, utilizing a recursive function. By assigning a strength rating to each player, their rankings were established, leading to varied probabilities of winning. It was decided to represent these abilities with randomly selected integers ranging from 1 to 21, with 1 denoting minimum strength and 21 denoting maximum strength. We explore hierarchical knockout tournament fixtures in competitions to develop optimal tournaments that enhance their attractiveness. In this study, we also performed calculations to determine the probability of each player winning in each round, thereby deducing which tournament fixture minimizes or maximizes the likelihood of the strongest player winning. In cases where the number of players is a power of 2, the first half comprises p/2 matches, where p is the total number of players. However, if the number of players is not a power of 2, k matches are played in the first round, with = 2r + , where 0 ≤ k < 2r, followed by implementing a balanced tournament fixture. The findings underscore the effectiveness of employing a balanced tournament fixture to maximize the probability of winning in a single-elimination tournament. Keywords: Single Elimination, Binary Tree, Dummy Players, Election Procedures, Hierarchically.