I haven't ever thought about taking a game with me on tour, but then I tend to tour alone. If I'm in need of a diversion, I'll use the solitaire game on my computer, but when I'm on tour, I don't even need that. Most of the time, I'm just too busy experiencing the places along the way and then writing about what I've seen and where I've gone.
If I were to take a trip with a friend, I might consider taking either a deck of cards or a travel-sized backgammon set. Either one would add little in the way of extra weight.