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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11683 |
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| _version_ | 1866909522146099200 |
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| author | Romão, Leonardo Gasparini de Paula, Samuel Plaça Ueda, Eduardo Takeo |
| author_facet | Romão, Leonardo Gasparini de Paula, Samuel Plaça Ueda, Eduardo Takeo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard Romão, Leonardo Gasparini de Paula, Samuel Plaça Ueda, Eduardo Takeo Computational Complexity 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. |
| title | Optimizing for aggressive-style strategies in Flesh and Blood is NP-hard |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2501.11683 |