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

TL;DR

This paper models aggressive strategies in Flesh and Blood as a combinatorial optimization problem, proving it is NP-hard and providing an ILP formulation for practical instances, thus revealing the game's computational complexity.

Contribution

It introduces the FAB problem, models it as a 0-1 Knapsack problem, and proves its NP-hardness, offering a new perspective on the game's strategic complexity.

Findings

FAB problem is NP-hard

ILP formulation for real-world instances

Complexity of simple strategies established

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.