Learning curves have been proposed as an adequate description of learning processes, no matter whether the processes manifest within minutes or across years. Different mechanisms underlying skill acquisition can lead to differences in the shape of learning curves. In the current study, we analyze the tournament performance data of 1383 chess players who begin competing at young age and play tournaments for at least 10 years. We analyze the performance development with the goal to test the adequacy of learning curves, and the skill acquisition theories they are based on, for describing and predicting expertise acquisition. On the one hand, we show that the skill acquisition theories implying a negative exponential learning curve do a better job in both describing early performance gains and predicting later trajectories of chess performance than those theories implying a power function learning curve. On the other hand, the learning curves of a large proportion of players show systematic qualitative deviations from the predictions of either type of skill acquisition theory. While skill acquisition theories predict larger performance gains in early years and smaller gains in later years, a substantial number of players begin to show substantial improvements with a delay of several years (and no improvement in the first years), deviations not fully accounted for by quantity of practice. The current work adds to the debate on how learning processes on a small time scale combine to large-scale changes.