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 off of 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, as well as the constant player count version are both intractable. However, we also show that two bounded versions of this decision problem -- deciding whether or not all players can complete their objectives -- can be solved in polynomial time.
翻译:在本文中,我们从算法组合游戏理论的角度研究合作纸牌游戏,即“团队:为九星球追寻”游戏。“团队:为九星球追寻”是一个基于传统游戏游戏游戏的游戏,以传统把牌游戏如桥或红心游戏为基础。在团队中,玩家被玩牌的手持牌,牌的颜色来自$C,价值在1美元至n美元之间。玩家还起草目标,与当前游戏中他们必须收集的一张牌相对应。玩家然后将每个玩牌的玩家转成一个把戏,由玩家玩家玩出最高价值卡的玩家来玩这个把戏和所有牌。如果所有玩家都完成了他们所有的目标,玩家就赢了。游戏还迫使玩家们不要谈论他们手中的牌,而牌牌的颜色是1美元到1美元到1美元之间的价值。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,以及固定的玩家计牌者数版本都是难的。然而,我们也可以将决定两个游戏的版本都无法解决。