Two experiments used Information Integration Theory to study how children judge expected value of complex gambles in which alternative outcomes have different prizes. Six-year-olds, 9-year-olds and adults (N = 73 in Study 1, N = 28 in Study 2) saw chance games that involved shaking a marble in a bicolored tube. One prize was won if the marble stopped on blue, another if it stopped on yellow. Children judged how happy a puppet playing the game would be, with the prizes and probability of the blue and yellow outcomes varied factorially. Three main results appeared in both studies: First, participants in all age groups used the normatively prescribed multiplication rule for integrating probability and value of each individual outcome — a striking finding because multiplicative reasoning does not usually appear before 8 years of age in other domains. Second, all age groups based judgment of overall expected value meaningfully on both alternative outcomes, but there were individual differences — many participants deviated from the normative addition rule, showing risk seeking and risk averse patterns of judgment similar to the risk attitudes often found with adults. Third, even the youngest children took probability to be an abstract rather than physical property of the game. Overall, in contrast to the traditional view, the present results demonstrate functional understanding of probability and expected value in children as young as 5 or 6. These results contribute to the growing evidence on children's intuitive reasoning competence. This intuition can, on the one hand, support surprisingly precocious performance in young children, but it may also contribute to the biases evident in adults' judgment and decision.