I sometimes have to endure my parents' or teachers' endless scolding, and sometimes endure endless lectures on boring things in school, and occasionally endure really long trips.
One way for me to deal with them is to do mental arithmetic, such as calculating squares and cubes, and approximating square roots and cube roots. Another is to do "make 24", which is just think up 4 numbers, and make 24 using add, subtract, multiply, and divide. Yet another (especially good if I'm in a room with wallpapers and carpets) is to stare at any symmetry pattern and visualize all the symmetries of the pattern like this (source)
(For example, I once classified all 17 wallpaper groups over the course of 20 hours of flight. The thought of classifying all 230 space groups is imposing, but if I ever need to take such a long flight again, I might work on it.)
Another one, which is less "systematic", but still fun, is doing some topological visualizations. For example, visualizing why the fundamental group of torus is abelian. Visualizing turning a 2-crosscap to a Klein bottle. Driving a Ferrari on a Sudanese Möbius band. And so on.
(I have yet to succeed in fully visualizing the Császár polyhedron. The Szilassi polyhedron, I can only barely visualize. Boy's surface is very difficult. And visualizing the eversion of sphere feels impossible.)
So, are there any other games I can use for such occasions? Such games should be possible to play without big calculations. Geometric things are usually good in this regard.
Edit: I remembered something called Conway's Soldiers. Apparently the protagonist in The curious incident of the dog in the night-time uses it for the same purpose... I should try it sometime.
Someone suggested playing chess or go in my mind. They are fine, but a bit complicated to hold in my head. I'm not good at chess or go. I'm ok at Hex, and even with Hex, I can't play a game in my head.
The game of Sprouts, however, is quite easy to hold in my mind. There are probably more games from Conway's Winning Ways for Your Mathematical Plays, that would be great as mental solitaire. I should read it one day.