The Hundred-Step Task

Chain arithmetic prices long-horizon autonomy in three short multiplications — and the price is steep.

A system that completes each step with probability 0.99 — a grade any benchmark would celebrate — succeeds at a hundred-step task with probability 0.99 multiplied a hundred times: about 0.37. Fewer than four runs in ten survive. Raise the step grade to 0.999 and the hundred-step chain still loses about one run in ten. Now invert the question: for ninety percent success over fifty steps, each step must clear roughly 0.998 — three-nines territory, far beyond any headline accuracy. The lesson reads in both directions. Forward: an agent demoed on brilliant single steps has demonstrated nothing about hours of unattended work. Backward: any claimed jump in autonomy should arrive as a whole-chain number — steps, completion rate, recovery behavior — and a vendor who reports only per-step scores has reported the flattering factor of a product they chose not to multiply.