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In this paper we study a cooperative card game called Hanabi from theviewpoint of algorithmic combinatorial game theory. In Hanabi, each card hasone among $c$ colors and a number between $1$ and $n$. The aim is to make, foreach color, a pile of cards of that color with all increasing numbers from $1$to $n$. At each time during the game, each player holds $h$ cards in hand.Cards are drawn sequentially from a deck and the players should decide whetherto play, discard or store them for future use. One of the features of the gameis that the players can see their partners' cards but not their own andinformation must be shared through hints.  We introduce a single-player, perfect-information model and show that thegame is intractable even for this simplified version where we forego both thehidden information and the multiplayer aspect of the game, even when the playercan only hold two cards in her hand. On the positive side, we show that thedecision version of the problem---to decide whether or not numbers from $1$through $n$ can be played for every color---can be solved in (almost) lineartime for some restricted cases.

Hanabi is NP-hard, Even for Cheaters who Look at Their Cards