Here’s a game fresh off the press for those who like 2-player abstract strategy games, especially ones played with a simple board and one type of piece.
Two players take turns placing or moving tokens in squares of an 8×8 board. No square may ever have more than 3 tokens, and tokens may only move up/down and left/right by one square. Each turn a player may add one token to any square the board or move any number of tokens from one square to an adjacent square (as long as at the end of that player’s turn there are <=3 tokens in each square).
Player 1 tries to make the sequence 1-2-3 in adjacent squares, player 2 tries to make 1-3-2. This includes diagonals, though pieces may not move diagonally. The first player to make their sequence wins.
Variations: changing sequences and square limits are an easy way to up complexity. Changing the dimensions of the grid (or using a different network, e.g. a hexagonal tiling) is another parameter which could be changed. For a 3-player variant, use 123, 132, and 213 as the goals. Additionally you could use multiple types of pieces (different colors say) and then make more complicated sequences.
Note: to prevent indefinite repeats, a player cannot make a move which would cause the other player to encounter an identical board state to what they just played on (e.g. if the other player moves a piece you cannot move it back).
If you solve this game I’ll give you a prize. If you then turn it into a variant which you can’t solve, I’ll bake you a cake.