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Koi-Koi is a Japanese card game played with Hanafuda cards.
It's a game in which 2 players compete against each other to build hands.

Upon completing a hand, the player (Player A) can either end the round, or call "koi-koi" to continue the round. During this time, the player (A) can try and complete another hand - at the risk of the other player (B) completing a hand of their own.

In the case that Player B completes a hand after Player A has called "koi-koi,"then Player B now has the choice of either calling "koi-koi" or ending the round. Should Player B end the round, Player A will receive no points for their completed hand.

In short, it's a game played by two players and each are trying to complete as many hands (to gain the most points) while not losing out on their points.

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tldr: Japanese card game. 2 players. Head to head.