Problem 3 The American chess master Harold Smith is playing the Soviet expert Vl
ID: 3204515 • Letter: P
Question
Problem 3
The American chess master Harold Smith is playing the Soviet expert Vladimir Kournikova 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, Smith has two possible approaches: to play a daring strategy or to play a conservative strategy. His probabilities of winning, losing, and drawing when he follows each strategy are shown in the table below. To maximize his probability of winning the match, what should Harold do?
Strategy
Win
Lose
Draw
Daring
0.45
0.55
0
Conservative
0
0.10
0.90
Strategy
Win
Lose
Draw
Daring
0.45
0.55
0
Conservative
0
0.10
0.90
Explanation / Answer
Giveh for winning the match, points scored by a person = 1
for draw = 0.5
for lose = 0
Probability of winning in a daring strategy
= 0.45 * 1 - 0.55 * 0 + 0 * 0.5 = 0.45
Probability of winning in conservative strategy
= 0 * 1 - 0.1 * 0 + 0.9 * 0.5 = 0.45
Now, since the both strategies have same chance of winning the game,
we can say probability that he wins a match in 2 games is 0.45
between two strategies he can follow any one if he wants to maximise the profit
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