Additive integration of information is ubiquitous in judgment and has been shown to be effective even when multiplicative rules of probability theory are prescribed. We explore the generality of these findings in the context of estimating probabilities of success in contests. We first define a normative model of these probabilities that takes account of relative skill levels in contests where only a limited number of entrants can win. We then report 4 experiments using a scenario about a competition. Experiments 1 and 2 both elicited judgments of probabilities, and, although participants' responses demonstrated considerable variability, their mean judgments provide a good fit to a simple linear model. Experiment 3 explored choices. Most participants entered most contests and showed little awareness of appropriate probabilities. Experiment 4 investigated effects of providing aids to calculate probabilities, specifically, access to expert advice and 2 simulation tools. With these aids, estimates were accurate and decisions varied appropriately with economic consequences. We discuss implications by considering when additive decision rules are dysfunctional, the interpretation of overconfidence based on contest-entry behavior, and the use of aids to help people make better decisions. (Contains 9 figures, 5 tables and 3 footnotes.)