We used to play a variant where White started with just 4 pawns and a King, but got to move twice on each turn.  Black started with the normal complement of pawns and pieces and could move only once.  The unassisted White King could checkmate the Black King (e.g., White king on e6, Black king on e8 was considered mate).

When my cousin showed me the chess moves as a very young boy he told me that you can either move 1 pawn 2 squares or 2 pawns 1 square. A lot of games we played started: 1.e3 and d3 1...e6 and d6 but mostly we liked 1.a3 and h3 vs 1...a6 and h6. Nobody wanted to move only one pawn if he could move 2...

To find out how moves count you should try "Progressive Chess" - White has one move, Black two, White three, Black four,... - usually the game ends after either "Black four" or "White five"