  Engaging in playful activities, such as playing a musical instrument,
learning a language, or performing sports, is a fundamental aspect of human
life. We present a quantitative empirical analysis of the engagement dynamics
into playful activities. We do so by analyzing the behavior of millions of
players of casual video games and discover a scaling law governing the
engagement dynamics. This power-law behavior is indicative of a multiplicative
(i.e., ``happy-get-happier'') mechanism of engagement characterized by a set of
critical exponents. We also find, depending on the critical exponents, that
there is a phase transition between the standard case where all individuals
eventually quit the activity and another phase where a finite fraction of
individuals never abandon the activity. The behavior that we have uncovered in
this work might not be restricted only to human interaction with videogames.
Instead, we believe it reflects a more general and profound behavior of how
humans become engaged in challenging activities with intrinsic rewards.
