Two players, Amy and Beth, take turns choosing numbers; Amy goes first. On her turn, a player may choose any number between 1 and 10, inclusive, and this number is added to a running total. When the running total of both play­ ers' choices reaches 100, the game ends. Consider two alternative endings: (i) the player whose choice of number takes the total to exactly 100 is the win­ ner and (ii) the player whose choice of number causes this total to equal or exceed 100 is the loser. For each case, answer the following questions:

(a) Who will win the game?

(b) What are the optimal strategies (complete plans of action) for each player?