Pushee

Pushee is a finite and drawless race game for two players.

Play is on a 5x5 board, with both players pushing in opposite directions. Each player has 5 pieces, numbered 1 through 5, which all start on their back row. It is suggested that the initial arrangement of pieces on the back row be selected randomly.

Players take turns pushing pieces forwards. A 'push' consists of pushing a piece one space forward, onto the space immediately ahead or the ones onto the left or right of that. A player may either push just the 1 piece forwards, or push forwards a piece and pull back the piece one size less onto any of the three squares behind it. For example, they may push forwards the 4 and pull back the 3, but not push forwards the 4 and pull back the 2, or just push forwards the 4 without pulling anything back.

A piece may not be pushed or pulled onto an occupied square, but a piece may push back a smaller opposing piece onto any of the three squares behind it. The person doing the pushing decides which square the opposing piece gets pushed onto.

The pieces moved on a single turn are considered to move simultaneously, so for example it's possible for the 2 and 1 to swap positions if the 1 is in front of the 2.

The first player to not have a legal move wins.