Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard
Leonardo Gasparini Romão, Samuel Plaça de Paula, Eduardo Takeo Ueda
TL;DR
This work formalizes aggressive, single-turn optimization in Flesh and Blood as the FAB problem and proves its NP-hardness by a reduction from the $0$-$1$ Knapsack problem. It then provides an Integer Linear Programming formulation to solve practical FAB instances and defines two variants, FAB-Aggro ($\lambda=0$) and FAB-Midrange ($\lambda=1$), to explore offense–defense trade-offs. The results reveal the intrinsic combinatorial complexity of resource management in FAB and motivate heuristic or approximation methods for real-time decision-making and game design. By connecting classic knapsack complexity to modern card-game strategies, the paper offers a foundation for algorithmic tools and design considerations that account for computational hardness in FAB-like games.
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.