Strategy in the game Go. Go is one of the oldest and most popular strategic board games in...

Strategy in the game Go. Go is one of the oldest and most popular strategic board games in the world, especially in Japan and Korea. The two-player game is played on a flat surface marked with 19 vertical and 19 horizontal lines. The objective is to control territory by placing pieces called stones on vacant points on the board. Players alternate placing their stones. The player using black stones goes first, followed by the player using white stones. [Note: The University of Virginia requires MBA students to learn Go to understand how the Japanese conduct business.] Chance (Summer 1995) published an article that investigated the advantage of playing first (i.e., using the black stones) in Go. The results of 577 games recently played by professional Go players were analyzed.

a. In the 577 games, the player with the black stones won 319 times and the player with the white stones won 258 times. Use this information to estimate the probability of winning when you play first in Go.

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b. Professional Go players are classified by level. Group C includes the top-level players, followed by Group B (middle-level players) and Group A (low-level players). The accompanying table describes the number of games won by the player with the black stones, categorized by level of the black player and level of the opponent. Estimate the probability of winning when you play first in Go for each combination of player and opponent level.

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c. If the player with the black stones is ranked higher than the player with the white stones, what is the probability that black wins?

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d. Given that the players are of the same level, what is the probability that the player with the black stones wins?

Source: Kim, J., and Kim, H. J., “The advantage of playing first in Go,” Chance, Vol. 8, No. 3, Summer 1995, p. 26 (Table 3).