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.

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

1. What are the optimal strategies for each player?

Consider a slight variant to the game. Now the player whose move empties the jar loses.

1. Does this game have a first-mover advantage?

2. What are the optimal strategies for each player?