By Nam Chi-hyung

There is a modern mathematical field called ``Combinatorial Game Theory'' that has been successful in finding the optimal solutions for various games. The games studied in combinatorial game theory are mostly two-person perfect-information games, especially those for which classes of positions for winning strategies can be stated explicitly, or at least proved to exist. Examples include not only simple games like ``Dots and Boxes,'' but also the most complicated game of all, Baduk.

Coupon Baduk, the topic of this lesson, is a sort of mathematical tool to learn the thoughts of professionals, about the size of the largest play at any time, and to quantify the sizes of specific moves, particularly toward the end of the game. It was devised by Elwyn Berlekamp, who has been a professor of mathematics and of electrical engineering/computer science at UC Berkeley since 1971, and who is better known to Baduk players around the world as the author of Mathematical Go.

The idea of Coupon Baduk is to compel the players to make quantitative decisions. The special device involved in playing Coupon Baduk is a stack of coupons. In other words, it's a Baduk game accompanied by a stack of coupons. The value of the coupons is uniformly spaced and they are sorted by descending value, with the most valuable coupons first. For example, there can be coupons with the values ranging from 10 to 0.5 in 0.5 point decrements.

At each turn, players may choose to take the top coupon, which will be added to his score at the end, OR he may instead make a play on the board. As usual, the game ends when all the coupons are taken and neither player wants to play any longer on the board. The result is decided by comparing the scores each player got on the board, plus the total of all the coupons he has taken.

The first game of Coupon Baduk was played in 1998 by Jiang Jujo and Rui Naiwei, the famous professional 9-dan couple. The games played by these two professionals provided documentation of expert opinions bounding the sizes of the moves they played, and in some cases, the mathematical techniques and theorems involved presented new information previously unknown to even the professionals.

Of course, while it is far too hasty to say that mathematics will conquer Baduk, its realm is steadily growing. Evidence of such improvement can be seen in that Prof. Berlekamp is coming to Korea to hold a Coupon Baduk tournament with promising young Korean professionals. It is scheduled between Nov. 28-29 with 6 prominent professional players including Sanghoon Hahn, the most famous 1-dan in the world after becoming a finalist for the LG Cup along with Sedol Lee 9-dan. This tournament is expected not only to provide many precious records, but also offer a good opportunity for Koreans to become familiar with the mathematical approach to Baduk.

chihyung@mju.ac.kr

The writer is a baduk professor at Myongji University and a professional player of the game.