Analyzing Three-Way Playoffs in the Sumo World.

This paper is concerned with tomoesen, a special method of three-way playoffs in the Japanese sumo world. In the tomoesen, only two wrestlers fight each other, with the third man resting for a while. Then, the winner of the first fight has to fight against the resting man. The former may be either a winner or a loser. This kind of fight will continue until there appears some one who bravely wins the two successive fights. Since the Pacific War ended, while more than 450 fights have been carried out, we have witnessed special tomoesen merely seven times. From a theoretical viewpoint, we can show that each of the men who come up to the ring has the victory probability of 5/14, and the third man, the probability of 4/14. The difference between those two numbers is 1/14 or 7.14286,,, . Although tomoesen is not a fair game in a strict sense, it has nevertheless been accepted by the public as an exciting sport game. It seems that there exists a reasonable balance between fairness and excitement. [ABSTRACT FROM AUTHOR]