Elroy and Judy play a game that Elroy calls the “race to 100.” Elroy goes first, and the players take turns choosing numbers between one and nine. On each turn, they add the new number to a running...

Elroy and Judy play a game that Elroy calls the “race to 100.” Elroy goes first, and the players take turns choosing numbers between one and nine. On each turn, they add the new number to a running total. The player who brings the total exactly to 100 wins the game.

(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?