The Crew: The Quest for Planet Nine is NP-Complete
Frederick Reiber

TL;DR
This paper analyzes the game The Crew: The Quest for Planet Nine, proving that its general decision problem is NP-Complete, while certain bounded versions are solvable in polynomial time, thus exploring its computational complexity.
Contribution
The paper formally models The Crew game and establishes its NP-Completeness in the general case, identifying tractable bounded variants.
Findings
General unbounded problem is NP-Complete.
Three bounded versions are solvable in polynomial time.
Provides a formal computational complexity analysis of the game.
Abstract
In this paper, we study the cooperative card game, The Crew: The Quest for Planet Nine from the viewpoint of algorithmic combinatorial game theory. The Crew: The Quest for Planet Nine, is a game based on traditional trick-taking card games, like bridge or hearts. In The Crew, players are dealt a hand of cards, with cards being from one of colors and having a value between 1 to . Players also draft objectives, which correspond to a card in the current game that they must collect in order to win. Players then take turns each playing one card in a trick, with the player who played the highest value card taking the trick and all cards played in it. If all players complete all of their objectives, the players win. The game also forces players to not talk about the cards in their hand and has a number of "Task Tokens" which can modify the rules slightly. In this work, we introduce and…
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Taxonomy
TopicsArtificial Intelligence in Games · Metaheuristic Optimization Algorithms Research · Constraint Satisfaction and Optimization
