artificial intelligence - How to form state space tree in a 2 player game same as billiards with alternate game turns -

i trying solve carrom board game ( same billiard game ) using ai techniques forming search tree. since game rule not giving strike turn again after pocketing, state space tree have depth 1 possible shots branches root. best approach solve kind of problems in ai chose best shot.

this looks simple minimax algorithm. expand search tree opponents view iteratively , calculate score states. opponent trying minimize score (which best him), try maximize score , choose action leads tree best score.