Victoria: Beating the House Using the Principles of Statistics and Randomness

This study presents the algorithm - Victoria - an approach that demonstrates there are parameters φ, k, j considered optimal that guarantee the player will always have an advantage over the house in sports betting field in the medium and long run with guaranteed satisfactory profits. After n Small Blocks (j n ) and Intermediate Blocks (IBs) containing k independent events with the same probability p, we conclude that the cost-benefit ratio over the value in a sequence of independent events β (success block) > ζ (failure block) is always the case. Taking into account the possible impacts of Victoria on Decision Theory as well as Game Theory, a function η(X t ) called “Predictable Random Component” was also observed and presented. The η(X t ) function (or fv(X t ) in the context of VNAE) refers to the fact that within a game in which the randomness factor in a uniform distribution is crucial to it, any player who has advanced knowledge of randomness added to other additional actions, whether with the support of statistics, mathematical, physical operations and/or other cognitive actions, will be able to determine an optimal strategy whose results of the expected value of the player's payoff will always be positive regardless of what happens after n sequences determined by the player. In addition, the possibility of the existence of a new equilibrium was also observed, thus resulting in the Victoria-Nash Asymmetric Equilibrium (VNAE) theorization. We develop a rigorous statistical foundation, incorporating Markov processes, Brouwer’s fixed-point theorem, and statistics convergence to validate the existence of asymmetrical advantages in structured random systems. And anchored by the Stirling Numbers, the Law of Large Numbers, the Central Limit Theorem, Kelly's Criterion, Renewal Theory, Unified Neutral Theory of Biodiversity, Nash Equilibrium and Monte Carlo simulation itself, for example, the proposed new equilibrium is expected to be a solid mathematical model suitable for modeling games in which one of the players tends to have asymmetric advantages. In this sense, VNAE is an extension of the classic Nash Equilibrium, Stackelberg Equilibrium, and Bayesian Equilibrium. Victoria has shown that by understanding the general behavior of randomness through statistics, we can, in a way, partially “predict” the future and shape it in our favor. Furthermore, in Game Theory, it is hoped that the impact could be relevant to better understanding and adapting concepts such as stochastic games, asymmetric games, zero-sum games, repeated games and imperfect information games, for example. By bridging gaps between theory and real-world applications, this work positions the VNAE as a foundational tool for interdisciplinary advancements in decision-making under uncertainty.