  Weiqi is one of the most complex board games played by two persons. The
placement strategies adopted by Weiqi players are often used to analog the
philosophy of human wars. Contrary to the western chess, Weiqi games are less
studied by academics partially because Weiqi is popular only in East Asia,
especially in China, Japan and Korea. Here, we propose to construct a directed
tree using a database of extensive Weiqi games and perform a quantitative
analysis of the Weiqi tree. We find that the popularity distribution of Weiqi
openings with a same number of moves is distributed according to a power law
and the tail exponent increases with the number of moves. Intriguingly, the
superposition of the popularity distributions of Weiqi openings with the number
of moves no more than a given number also has a power-law tail in which the
tail exponent increases with the number of moves, and the superposed
distribution approaches to the Zipf law. These findings are the same as for
chess and support the conjecture that the popularity distribution of board game
openings follows the Zipf law with a universal exponent. We also find that the
distribution of out-degrees has a power-law form, the distribution of branching
ratios has a very complicated pattern, and the distribution of uniqueness
scores defined by the path lengths from the root vertex to the leaf vertices
exhibits a unimodal shape. Our work provides a promising direction for the
study of the decision making process of Weiqi playing from the angle of
directed branching tree.
