A Reciprocal Model of Practice and Skill - Navigating between Dropout and Expertise

We present a formal model of free-learning where skill and practice form a feedback-loop, integrating previous work on learning, forgetting and motivation.  Through model simulations and empirical data from online chess (N>10,000) and adaptive learning systems (N>100,000), we show that S-shaped learning curves are risky for dropout and suggest interventions.