The other day before class, I introduced a little game called Sprouts. I found the rules summarized at the MAA website. There is also a nice discussion on the Science News website. I find it interesting that such a simple game can be analyzed using mathematical properties.
One of my favorite "math" games is a game called Eleusis. This game was invented Robert Abbott as an analogy of the scientific method. So perhaps we should call this a "science" game. The game is played with a deck (or multiple decks) of playing cards. I turn over the first card and then think of a pattern that would start with that card. Now, the remaining players take turns attempting to choose a card from their hands that they believe would be a valid next card in the pattern. If they are correct, I leave it there. If they are incorrect, I move the card out of the sequence and below the card they tried to follow (for future reference).
The goal for the players is to eventually arrive at a hypothesis that they believe explains the pattern. By playing cards, they attempt to critically assess whether their hypothesis is a complete explanation of the pattern. This mimics the scientific method because we see patterns in how nature functions, and through experiment we attempt to see if controlled efforts are consistent with or contradict our acting hypotheses.
Try it out? Let me know how the game goes.