Page 29 - KVIS Book

MAT02A, MAT04I

On the Probability of Elimination in Tournament

Nathawuth Wongwutcharanukoun, Jirayus Jinapong
Kamnoetvidya Science Academy, Thailand
Supervisor: Guntaphon Tassanasophon
Email: 5900022@kvis.ac.th

Recently, there are many competitions in the world and those competitions are
classified into many types. One of them is called a tournament. The tournament that
we study is called the single-elimination tournament where the loser of each match-up
is immediately eliminated from the competition. The winner goes to the next round
until the final match-up, whose winner becomes the champion of the tournament. For
this process, if 2 teams that have high performances against to each other in the first
round, one team will be eliminated and get reward from of the first round even though
they can get higher reward from higher round. So, there is a system, called format, to
help the tournament arranging all teams into the brackets of the tournament. A
condition that we use to control the winning of each game is a ranking of each team in
the tournament. In this research, we investigate the probability that each team will be
eliminated in each round with different formats, and then we compare the results to
find the best format. Moreover, we also concern about the number of matches that is
used for each format. Finally, we found formulas of the probability of the 2-group,
round-robin and random formats. For 4-group and 8-group formats, we found the
diagrams.

Keywords: tournament, team, format, rank