Elroy and Judy play a game that Elroy calls the “race to 100.” Elroy goes first, and the players…

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.

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(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?

 

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