5. Mr. Bemard and Mr. Meyer go out to lunch and play a game called "One Hundred". Each player puts $50 in an envelope. Then, Mr. Bernard goes first, and the players take turns choosing numbers between one and nine. On each tum, the new number chosen is added to the previous total. The player who can bring the total to exactly $100 wins all the money. In games like this, there is often a first-move advantage or a second-move advantage. If both Mr. Bernard and Mr. Meyer play optimally, who should end up winning this game? Explain your reasoning. Hint: start at the end of the game and work backwards toward the start of the game! a. b. Identify the optimal strategies (complete plans of action) for each player?

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5. Mr. Bernard and Mr. Meyer go out to lunch and play a game called "One Hundred". Each player puts $50 in
an envelope. Then, Mr. Bernard goes first, and the players take turns choosing numbers between one and
nine. On cach turn, the new number chosen is added to the previous total. The player who can bring the
total to exactly $100 wins all the money.
In games like this, there is often a first-move advantage or a second-move advantage. If both Mr.
Bernard and Mr. Meyer play optimally, who should end up winning this game? Explain your
reasoning. Hint: start at the end of the game and work backwards toward the start of the game!
a.
b. Identify the optimal strategies (complete plans of action) for each player?
Transcribed Image Text:5. Mr. Bernard and Mr. Meyer go out to lunch and play a game called "One Hundred". Each player puts $50 in an envelope. Then, Mr. Bernard goes first, and the players take turns choosing numbers between one and nine. On cach turn, the new number chosen is added to the previous total. The player who can bring the total to exactly $100 wins all the money. In games like this, there is often a first-move advantage or a second-move advantage. If both Mr. Bernard and Mr. Meyer play optimally, who should end up winning this game? Explain your reasoning. Hint: start at the end of the game and work backwards toward the start of the game! a. b. Identify the optimal strategies (complete plans of action) for each player?
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