Pen-and-paper educational games I'm teaching maths at the 8-16 year level, one-on-one tuition.
What are some good pen-and-paper maths games I can play with these kids?
Googling "math games" just gets me a load of interactive animated junk and most games in this list are not actually educational and most are not really mathematical either (in the high-school-level sense -- they are combinatorial games).
It's important that these games teach or give exercise in something other than arithmetic.
Ideally these games would have an element of competition (teacher and pupil racing to complete something, for example) but I need to be able to invent instances of the game in just a moment's thought.
Any ideas?

We used to do this in my high school math class. I am not sure if it is too much of lower-level math, but we had to take the numbers from the year (i.e. 2, 0, 1, and 9) and then make equations that are equal to the numbers 0 through 2019 (or whatever year it is) using each number only once, but any mathematical functions... It's easy for some numbers, but pretty difficult for others. I realize it is mostly arithmetic but still a cool warm-up math game.
