8 Consider the following 5stone game Rules Player A starts t

8. Consider the following 5-stone game: Rules: Player A starts the game. Each player is allowed to take 1 or 2 stones at the turn. Player B is allowed to “pass” (take 0 stones) once during the game. Outcome: Player who takes the last stone wins the game Draw the game tree representing all possible outcomes of the game. Highlight the likely path of the game. (8 points)

Solution

Algorithm for drawing the tree:

The first turn is of A. Therefore, draw two nodes, one where A picks 1 stone and one where A picks 2 stones

The next turn is of B. Therefore, draw 3 nodes from each node of A. One where B picks 0 stones, one where B picks 1 stone, One where B picks 2 stones

The next turn is of A again, Therefore, draw two nodes from each node at the bottom of the tree, one for 1 stone and one for 2 stones.

Repeat the same, alternating between A and B each time. When a sum over the line has reached 5 stones, terminate it.

Assuming an equal probability for draw, assign a probability of 0.5 to each division during a and 0.33 to each division during B.

The path with maximum probability is the likely path of the game