GAME THEORY QUESTION

Ahmet and Betl simultaneously call out one of the colors 'white' or 'red'. If they have both chosen 'white' Ahmet wins the game and he receives 3 TL from Betl. If the chosen colors are different, then Betl wins and Ahmet pays 2 TL to Betl. If they both choose 'red', then there are three possibilities:

- with probability 1/3, game terminates without any payement,

- with probability 1/2, game is played once more,

- with probability 1/6, players switch their roles and the game is played once more.

Find value of the game and determine the minmax strategies of players.