Two players, Amy and Beth, play the following game with a jar containing 100 pennies. The players…

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.

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(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?

 

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