Probability transformation functions were introduced into modelsof behavior toward risk to allow them to accommodate violations of the expected utility hypothesis.This paper examines the shape of the probability transformation function, its interpretation asoptimism or pessimism, and how the ranking of outcomes becomes important when probability transformationsare used. It also explores two behavioral implications: the overweighting of unlikely, extremeoutcomes, and intertia around certainty. Finally, the rationality of transforming the probabilitydistribution is discussed.