Consider a slight variant to the game in Exercise U5. Now
the player whose move empties the jar loses.
(a) Does this game have a first-mover advantage?
(b) What are the optimal strategies for each player?
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.)
(a) 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.
(b) What are the optimal strategies (complete plans of
action) for each player?