Consider the two$-$player game whose starting conguration is shown in the figure below. Player A moves first. The two players take turns moving, and each player must move his token to an open adjacent space in either direction. If the opponent occupies an adjacent space, then a player may jump over the opponent to the next open space if any. For example, if A is on square $3$ and B is on square $2,$ then A may move back to square $1.$ The game ends when one player reaches the opposite end of the board. If player A reaches square $4$ first, the value of the game to A is $+1$; if player B reaches square $1$ first, the value of the game to A is $-1.$