In two experiments, 330 3- to 4-year-olds competed for stickers in a game in which the optimal response strategy was to point to an empty box that their opponent would receive in order to obtain a baited box for themselves. When the baited box contained stickers, children showed a strong tendency to point at the baited box and therefore lose the stickers to their opponent. In Experiment 1 children performed better when the number of stickers to be won was represented with one of five different types of symbol: numerals, number words, dots, a photograph or sweets. In Experiment 2 children transferred their improved performance in symbolic conditions to non-symbolic conditions. These findings suggest that symbols enable children to formulate an efficient response strategy, and that this effect may be qualitatively different in children from the effect of symbols in non-human primates.