Sprouts

Sprouts is a pencil-and-paper topology game invented in 1967 by mathematicians John Conway and Michael Paterson at Cambridge. Starting with a few dots, players take turns drawing a curve connecting two dots (or a loop at one dot) with the constraint that curves don't cross previous curves; each new curve gets a new dot in its middle; and no dot can have more than three lines emerging from it. The player who cannot move on their turn loses. Wonderfully deep for such a simple game.