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 $c$ colors and having a value between 1 to $n$. 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 formally define a perfect-information model of this problem, and show that the general unbounded version is computationally intractable. However, we also show that three bounded versions of this decision problem - deciding whether or not all players can complete their objectives - can be solved in polynomial time. \end{abstract}
翻译:在本文中, 我们从算法组合游戏理论的角度研究合作牌游戏, “ 团队: 追寻九星球 ” 。 团队: “ 追寻九星球 ” 是一个基于传统的把戏纸牌游戏的游戏, 比如桥或心。 在团队中, 玩家会得到一张牌的手, 牌来自1美元, 价值在1美元到 美元之间。 玩家们还起草目标, 与当前游戏中必须收集的一张牌相对应。 玩家们然后把每个玩一张牌的玩一个把戏, 玩家们会把戏和所有玩牌的玩家一起玩。 如果所有玩家都完成了他们所有的目标, 玩家会赢。 游戏还迫使玩家们不要谈论他们手中的牌, 并且有一些“ Task Tokens”, 这可以稍稍修改规则。 在这项工作中, 我们介绍并正式定义了这个问题的完美信息模型, 并显示通用的无线版本是无法计算的。 但是, 我们还显示三个有固定的游戏者 能够解决全部决定 。