I have been enjoying some of the (simpler) mathematical explorations of simple games on numberphile with the sadly recently-passed Elwyn Berlekamp.
Dots and Boxes I remember from my childhood. I also taught my kids a few years back. When you see strategies formalised its fascinating!
Amazons is a game I didn’t know but sounds intriguing.
Maybe something to teach Google Deepmind?
Incidentally – Numberphile is one of my favorite youtube channels. I highly recommend!