Step accuracy alone does not determine long-horizon execution reliability

For a fixed horizon, the probability that every local check passes can be written as a product of conditional probabilities given all earlier passes. Replacing every conditional factor with one marginal accuracy assumes additional structure. An action changes the environment and the agent's later observations, so errors are often not independent identical events. A wrong account selection can affect every later action; a transient rate-limit response can trigger a recovery branch. An average measured only on easy successful prefixes is especially poor evidence for later difficult states.

Long-horizon benchmarks such as WebArena and AgentBench expose multi-step execution problems, but their results do not justify a universal per-step error law. Define the event unit: tool call correctness, subgoal completion, monitored property, or final outcome. A harmless exploratory action need not have a unique correct label. Fixed-horizon reasoning is easiest in controlled examples; real early termination leaves later opportunities unobserved. Do not count missing later steps as correct or estimate all conditional probabilities from the selected subset of trajectories that survived far enough.

Without a dependence model, marginal error probabilities imply only bounds on the chance of some error. Perfectly shared errors can occur together in a small fraction of episodes, leaving many flawless episodes but severe failures in the affected ones. Errors spread across disjoint episodes can instead ensure that nearly every episode has at least one. Independence lies between those possibilities in many examples. Therefore positive correlation does not automatically lower every perfect-path probability relative to independence, even though common-cause failures can be especially damaging for particular tasks and risk criteria.

Linearity of expectation still gives an expected error count from valid marginal probabilities without requiring independence. That count does not determine the probability of zero errors, the severity of an error, or whether recovery succeeds. Separate local detect-and-repair behavior from irreversible effects and final constraints. A confirmation step can reduce some failures while adding work and a new potential failure mode. Evaluate the actual recovery policy and its resource budget rather than multiplying a detector's and repairer's marginal accuracies without conditional or joint evidence.

Stratify evaluations by task structure and opportunity count while preserving full outcomes and budgets. Inspect whether failures concentrate after shared observations, a tool-schema change, or a common policy misconception. Report time to first decisive failure and successful recovery frequency with explicit denominators. Longer traces can have more opportunities for error but also reflect harder tasks or inefficient policies, so an uncontrolled relation between length and failure is not a causal law. Use controlled interventions or matched tasks when assessing the effect of adding a verification or recovery stage.

The Markov lab supplies one explicit absorbing-failure model. Reset, explicitly set BOTH p=0.1 and q=0, predict state-one probability 0.3439 after four transitions, then Play or Step four times to t=2. Reset and re-set BOTH p=0.2 and q=0; predict 0.5904. Both start in state zero; n=min(2000000,floor(2 t)), and edits retain t. State one is absorbing only because q=0. This exact discrete chain assumes its transition law; it is not an agent, arbitrary correlated-error process, or proof that real task success follows the same hazard.