Synergy Magic Chess Optimization for 3 Evolution with Binary Integer Programming

The study explores the application of mathematical optimization techniques to improve strategic decision-making in the Magic Chess mode of the game Mobile Legends: Bang Bang. The primary objective is to develop a systematic method for achieving high-level hero synergies, specifically focusing on the "3 Evolution" tier, which requires precise hero selection and resource management within the game’s constraints.

The research utilizes Binary Integer Programming (BIP) to model the selection process. By defining binary variables—where a value of 1 indicates a hero is selected for the lineup and 0 indicates they are excluded—the model effectively navigates the limitations of available hero slots and the specific requirements for desired synergies. The methodology employs the QM for Windows v5 software to solve the objective function, which is designed to minimize the number of heroes required to reach the target synergy level.

By framing hero selection as a constrained optimization problem, the findings provide a structured approach for players to maximize their tactical efficiency. The model demonstrates that mathematical modeling can successfully translate complex game mechanics into actionable strategies, allowing players to optimize their lineups while adhering to the game's evolving rules and slot limitations. This approach offers a quantitative alternative to traditional trial-and-error gameplay, providing a rigorous framework for competitive strategy in the Magic Chess environment.