This paper investigates the relationship between the possession of some of the reasoning abilities required to play digital mind games and the school performance of primary school pupils. It draws on an in-field experiment involving 60 Italian primary school children; the experiment was based on the use of the standardized test LOGIVALI which foresees ten one-hour gaming sessions with five mind games. The pupils were divided in three groups according their school achievement (high, medium and low achievers) and their performance at the test was studied; a substantial consistency was found between school achievement and ability to solve the adopted digital games. A closer insight was also given into the specific reasoning abilities actually possessed by the three different categories of pupils, thanks to the fact that the LOGIVALI test also allows a finer distinction among the different types/levels of reasoning abilities required to perform the proposed gaming tasks.