Board games belong in the mathematics classroom because they are a celebration of problem solving... and problem solving is at the heart of a quality mathematics education.
Dvonn, Tzaar and Santorini are all high rated strategy games on board game geek (boardgamegeek.com) which is the best online resource for board games. My fourth recommendation, Inverse, does not get a high rating, but for the math classroom, this game is top notch.
This video describes how to play Santorini and suggests that your classroom adopt it, or one of the other three strategy games.
You can find eight godly powers here:
www.mathpickle.com/K-12/MathPickle_Podcast/Entries/2011/9/7_Santorini.html
Bias Alert: Santorini is my game. Dvonn and Tzaar are designed by Kris Burm. Inverse is designed by Niek Neuwahl.