Since having two small children, I have spent quite a lot a time playing with their toys (normally with the children). Then, perhaps as the boredom sets in, I thinking about the principles underlying the games.
Mathematicians tend to enjoy games as they can offer well defined problems with relatively simple rules leading to a (sometimes complex) range of outcomes. Games such as go, chess, connect four, poker, etc. have been very well studied; the games I'm looking at are a bit less academic. No doubt they have been studied at some point, but this is my take on those games.
These post are mainly just some explorations of various ideas. Normally I try to simplify the game to its bare bones and then see what happens as it get more complicated. None of these posts are complete or at all rigorous.