Fairness in Games: A Study on Children's and Adults' Understanding of Probability

This study aims to analyse the reasoning that children and adults with the same school level use to assess and justify the fairness of games, considering aspects of probability such as randomness, sample space, and comparison of probabilities. Data collection included a Piagetian clinical interview based on games of chance. The results showed that the participants' judgments about the fairness of the games depends mainly on the understanding about independence of events, analysis of the sample space, and perception of proportionality when comparing probabilities, and that they have misunderstandings about these ideas. The similar low performance of adults and children on probabilistic reasoning, indicates that the maturity and experience of these adults were not enough to properly develop probabilistic reasoning and to instrumentalize it to assess the fairness of a game consistently. Thus, teaching interventions to expand and consolidate students' learning in the field of probability are recommended and the activities presented in this study may serve as a basis for such interventions.