Solution-What are the optimal strategies for player

What are the optimal strategies for player

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Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 40 matchsticks, and Fred goes first. On each turn, each player may remove one, two or three matchsticks. The player to remove the last matchstick wins the game.

(i) Suppose there are only five matchsticks left and it is Barney's turn. What move should Barney make to guarantee himself victory? Explain your reasoning.

(ii) Suppose there are 10 matchsticks left and it is Barney's turn. What move should Barney make to guarantee himself victory?

(iii) Now start from the beginning of the game (40 matchsticks, Fred to make a move). If both players play optimally who will win? Is there any "first mover advantage"?

(iv) What are the optimal strategies for each player?

Reference no: EM132548731

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What are the optimal strategies for player

Reference no: EM132548731

Reference no: EM132548731

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