Model the following game as an adversarial search poblem. Your modeling should be complete and detailed specifying state representation, actions, terminal test, state values, cutoff evaluation, etc....

Extracted text: Model the following game as an adversarial search poblem. Your modeling should be complete and detailed specifying state representation, actions, terminal test, state values, cutoff evaluation, etc. There is a board that has six holes. There is a total of 20 small balls that are distributed in the holes randomly provided that no hole is empty. The game is played in turns by two players. In each player's turn, the player can remove any number of balls from ONE HOLE ONLY. The player that removes the last ball from the board loses the game.