Under the normative Expected Value (EV) model, multiple outcomes are additive, but in everyday worth judgement intuitive averaging prevails. Young children also use averaging in EV judgements, leading to a disordinal, crossover violation of utility when children average the part worths of simple gambles involving independent events (Schlottmann, 2000). This study explored the origins of this averaging bias in children's worth judgements, assessing whether averaging also appears for riskless judgements and for other types of risky judgements. In Experiment 1, 8-year-olds judged the worth of having either one or two squares of chocolates in two formally equivalent tasks: Children made additive worth judgements when chocolates varied in size, but used averaging when they varied in winning probability. Performance on the EV task was slightly more advanced when risky followed riskless judgements, with some evidence of transfer. In Experiment 2, 5-year-olds gave additive worth judgements when judging variable fractions of chocolate pies, with displays closely parallel to the spinner discs used for the gambles in Experiment 1. In Experiment 3, 5-year-olds gave additive worth judgements of gambles in which to win either one or two prizes, with alternative rather than independent probabilities of winning. Thus the overgeneralisation of averaging processes to EV judgement, while persistent, neither reflects a general difficulty with additive value judgement, nor with displays showing positive and negative information, nor with risky judgement per se. It may come into play because children have difficulty appreciating the implications of independence, apparent also in other domains. Despite such difficulty, children realize that risky game outcomes go beyond what they can see, and so may apply averaging, as default strategy for population judgement, whereas addition might be the default for judging the sample itself. (Contains 5 figures and 1 table.)