There are lots of games that are explicitly and implicitly mathematical. Some a great and some are terrible.
Math Mama Writes has introduced me to some of the great ones. Math for Love has a great post cautioning us that any game labeled as a "fun math game" is like calling something you would ingest a food product--typically not a good sign.
If your goal is to teach and you just slap the word “fun” on at the end, you end up with garbage. On the other hand, if you’re focused on making a game that’s really good, well, then it is fun. Of course, whether it has any educational value is pretty dubious.I've played mathy games for many years. There are hundreds (never mind the hundreds more using nothing more than a deck of cards). Here are 20 (and please add your own favorites in the comments):
I find these games to be fun first, and mathematical second. I use some of these in my classroom and a few to complement or inspire content. For example, there are some great counting questions that can be asked about Set:
How many cards are in the deck?
How many sets are in the deck?
What's the greatest number of cards you can have without a set?
I've used Mastermind lessons as a tool to develop the concept of proof with middle schoolers. Backgammon is a great game to practice probability.
Overall, though, many of these games present challenges in the classroom: they take too long to play or teach the rules, they require too much set up, they can only be played by a limited number of people, students can play without actually trying to implement any thoughtful strategy, and the big one: it is challenging to convince kids (and schools and parents) that playing these games is not just an extra, froofy, free time activity and a break from doing "real" math. True, becoming better at chess will most likely not help you become better with fractions, but I've begun to think about how these above games could help develop mathematical thinking and habits of mind.