In many decision tree problems, the decision maker\'s goal is to maximize the pr

Question

In many decision tree problems, the decision maker's goal is to maximize the probability of a favorable event occurring. To incorporate this goal into a decision tree, simply give a reward of 1 to any terminal branch that results in the favorable event occurring and a reward of 0 to any terminal branch that results in the favorable event not occurring. Then maximizing expected reward is the same as maximizing the probability that the favorable event will occur. Use this idea to solve the next problem The American chess master Jonathan Meller is playing the Soviet expert Yuri Gasparov in a two-game exhibition match. Each win earns a player one point, and each draw earns a half point. The player who has the most points after two games wins the match. If the players are tied after two games, they play until one wins a game; then the first player to win a game wins the match. During each game, Meller has two possible approaches: to play a daring strategy or to ply a conservative Strategy. His probabilities of winning, losing, and drawing when he follows each strategy are shown in table 10. To maximize his probability of winning the mater, what should the American do?

Explanation / Answer

According to the given data, being conservative only leads to loss with probability 0.10 and a draw with 0.90 probbaility.

But being Daring increases the probability of winning, to 0.45

So, to maximize the probability of winning the match, the American should be daring.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.