Mini-Games

Although I learned chess at a fairly young age (6 or 7), it took me another 10 years before I began to play seriously. In the meantime I played a number of 'simpler' games, although they did have 'chess' like features (two players, turn based play etc). These included Nine Men's Morris, Feudal and Connect 4. Often these were played during the school holidays, either with my brother, or with friends. Although the results of these friendly matches are long forgotten, but I do think they helped me develop the kind of thinking that I used when starting my chess career.
Of course there a number of games which fall between the simplicity of noughts and crosses and the complexity of chess/go/shogi. One such game is an invention of IM Ken Regan, dating back to his time as a student at Oxford University. It is a checkers like game, although no pieces are actually captured. Instead the goal is to run your opponent out of moves. He describes it in detail in a post about AlphaZero  as an example of a game is small enough to be solvable, but large enough that this cannot be done too quickly.
I find games of this nature quite interesting, as it is far easier to test the success of players strategies (both human and computer). As the search space is smaller, the number of good and bad ideas is much more manageable for the human brain. However, two evenly matched players should be able to challenge each other, as what may work most of the time, might not work *all* the time.