A probability-adjustment task was presented to 6–14-year-old children. In 2 experiments, children had to generate equal probabilities by completing the missing beads in a target urn with 1 type of beads presented beside a full urn with both winning and losing beads. The task was embedded in a competitive game. This relevant-involvement method secured optimal understanding and motivation. The analysis was based on number of matches with, and sum of distances from, the correct response and the predictions of other strategies. The results indicate that only at around the age of 13 did most children proportionally integrate the 2 dimensions (i.e., the numbers of winning and losing beads). The youngest sometimes relied on 1 dimension, and 9- and 10-year-olds partly combined the 2 types of quantities additively. The cognition involved in probability adjustment was analytic rather than global or intuitive. The ability to generate equal probabilities is discussed in terms of the many faces of probability.