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The Mackey-Glass system is a well-known model used to explore complex delayed dynamics, characterized by the multistability, i. e. the coexistence of multiple periodic and chaotic attractors. Predicting the long-term evolution of such systems is highly challenging due to their infinite-dimensional nature, where initial conditions must be defined as functions over a time interval. In this work, we introduce an extension of the recently proposed basin entropy method to randomly sample high-dimensional spaces. By combining this stochastic approach with the analysis of basin fractions, we uncover the intricate structure of the basins of attraction and their boundaries. Our results provide new insights into the predictability of these systems and offer indicators for detecting critical changes, or bifurcations, in the dynamics. These methods offer promising tools for studying the behavior of other complex, infinite-dimensional systems.