Why completion rates fall faster than step counts rise

If each step of an agent task succeeds independently with probability p, a task requiring n steps succeeds with probability p to the power n. The consequence is unintuitive until it is written down: a per-step success rate that sounds excellent produces a poor end-to-end rate once a chain runs to twenty steps.

At a per-step rate of 0.99, a four-step task completes about 96 percent of the time and a twenty-step task about 82 percent. At 0.95 per step, the same two figures are roughly 81 percent and 36 percent. The model has not become worse. The chain has become longer.

Real failures are also correlated rather than independent, which usually makes matters worse than the arithmetic suggests. An ambiguous identifier resolved incorrectly at step three is not an isolated error; every subsequent step operates on the wrong record and does so correctly.

This is why the design advice that survives contact with production is unglamorous: shorten chains, checkpoint state so a retry does not repeat an early error, verify intermediate results where verification is cheap, and route irreversible actions through a human.

It also explains a persistent gap in perception. Demonstrations use short, clean chains, where the arithmetic is forgiving. Deployments use long, messy ones, where it is not.