It has long been observed that players in experimental games differ in their strategic ability. In particular, some players seem to lack any strategic ability whatsoever. These non-strategic players have not however been analyzed per se to date. Using a controlled experiment, we find that half of our subjects act non-strategically, i.e. they do not react to significant changes in the environment. We explore why these subjects perform so poorly. Our design allows us to rule out a number of widespread explanations such as lack of attention, misconception or insufficient incentives. Using reaction time information, we find that these subjects do actually pay attention to relevant changes in the environment, but fail to process this information in an appropriate manner. This inability to act strategically is a robust finding in the sense that it transfers across games. Last, bearing in mind that our subjects are chess players recruited from an international tournament, we ask why their strategic chess-playing ability does not transfer to laboratory games. JEL classification: D81, D03, C91.