We have this game:
Clarifications:
- Pawns can move and take across sides.
- Pawns can't jump over other pieces when moving by two squares.
- "Forward" means from the middle of your side towards the middle of your opponent's side, therefore, the middle pawn can initially move in all four directions, but can never return to its starting square once it has been moved.
- A pawn can move two spaces multiple times provided it is still on its starting side.
- En passant is not allowed
Is there a position on the cube, in which the game inevitably leads to a draw (none of the players can win) if both players play perfectly?