In a contest, participants spend money or effort to increase their chances of winning a prize. The authors examine primarily the following question: Could the timid (the more risk averse) have a better chance of winning in contests? Under limited liability the answer is always positive. In the absence of limited liability there is no single answer, whereas when the prize is shared as a function of effort the outcome is independent of the contestants' risk aversion. The authors also relate their results to self-protection and examine some other implications of risk aversion. Copyright 1995 by Royal Economic Society.