The paper studies a repeated contest when contestants are uncertain about their true abilities. A favourable belief about one's own ability (confidence) stimulates effort and increases the likelihood of success. Success, in turn, reinforces favourable beliefs. We consider a specific example in which this reinforcement mechanism implies that players fail to learn their true abilities, and that one player will eventually win the contest forever. As a consequence, persistent inequality arises, and the worse player may eventually prevail. Furthermore, confidence is self-serving in that it increases a player's utility and the likelihood to be the long-run winner.