  The ability to estimate task difficulty is critical for many real-world
decisions such as setting appropriate goals for ourselves or appreciating
others' accomplishments. Here we give a computational account of how humans
judge the difficulty of a range of physical construction tasks (e.g., moving 10
loose blocks from their initial configuration to their target configuration,
such as a vertical tower) by quantifying two key factors that influence
construction difficulty: physical effort and physical risk. Physical effort
captures the minimal work needed to transport all objects to their final
positions, and is computed using a hybrid task-and-motion planner. Physical
risk corresponds to stability of the structure, and is computed using noisy
physics simulations to capture the costs for precision (e.g., attention,
coordination, fine motor movements) required for success. We show that the full
effort-risk model captures human estimates of difficulty and construction time
better than either component alone.
