Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard

Leonardo Gasparini Romão; Samuel Plaça de Paula; Eduardo Takeo Ueda

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arXiv · 2501.11683

Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard

Leonardo Gasparini Romão·Samuel Plaça de Paula·Eduardo Takeo Ueda

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Abstract

Flesh and Blood (FAB) is a trading card game that two players need to make a strategy to reduce the life points of their opponent to zero. The mechanics of the game present complex decision-making scenarios of resource management. Due the similarity of other card games, the strategy of the game have scenarios that can turn an NP-problem. This paper presents a model of an aggressive, single-turn strategy as a combinatorial optimization problem, termed the FAB problem. Using mathematical modeling, we demonstrate its equivalence to a 0-1 Knapsack problem, establishing the FAB problem as NP-hard. Additionally, an Integer Linear Programming (ILP) formulation is proposed to tackle real-world instances of the problem. By establishing the computational hardness of optimizing even relatively simple strategies, our work highlights the combinatorial complexity of the game.

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Leonardo Gasparini Romão, Samuel Plaça de Paula, Eduardo Takeo Ueda. 2025-01-20. Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard. https://arxiv.org/abs/2501.11683

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