Assignment task: Kermit and Fozzie play a game with two jars, each containing 100 pennies. The players take turns; Kermit goes first. Each time it is a player's turn, he chooses one of the jars and removes anywhere from 1 to 10 pennies from it. The player whose move leaves both jars empty wins. (Note that when a player empties the second jar, the first jar must already have been emptied in some previous move by one of the players.)
1. Does this game have a first-mover advantage or a second-mover advantage? Explain which player can guarantee victory and how he can do it. (Hint: Simplify the game by starting with a smaller number of pennies in each jar, and see if you can generalize your finding to the actual game.)
2. What are the optimal strategies for each player? (Hint: First think of a starting situation in which both jars have equal numbers of pennies. Then consider starting positions in which the two jars differ by 1 to 10 pennies. Finally, consider starting positions in which the jars differ by more than 10 pennies.)