Two players, Amy and Beth, play the following game with a jar containing 100 pennies. The players take turns; Amy goes first. Each time it is a player’s turn, she takes between 1 and 10 pennies out of...

Two players, Amy and Beth, play the following game with a jar containing 100 pennies. The players take turns; Amy goes first. Each time it is a player’s turn, she takes between 1 and 10 pennies out of the jar. The player whose move empties the jar wins.

(a) If both players play optimally, who will win the game? Does this game have a first-mover advantage? Explain your reasoning.

(b) What are the optimal strategies (complete plans of action) for each player?