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The arm band is known as the Pra Jiad (Thai: ประเจียด).
Both are essential to the spectacle of a Muay Thai bout, along with the pre-fight pageantry that is unique to this ancient Thai fighting art.
Competitors wear arm bands in Muay Thai primarily because it is a part of the Thai tradition. It has been handed down from the time when Muay Thai was used in warfare.
Many fighters also wear the Pra Jiad because they believe that it brings them good luck in their fights.