← All parts of this equation

Equation 12 · Part 3 · Reliable AI Agents Are Control Systems, Not Chatbots

Symbol p_i

Pr⁡(task success)=∏i=1npi.\Pr(\text{task success}) = \prod_{i=1}^{n} p_i.
pip_i

What this part means

pip_i is an input to the expression that computes the quantity on the left.

Its job in the formula

pip_i is an input to the expression that computes the quantity on the left.

The passage around this formula

Single-turn model quality can hide long-horizon fragility. Suppose a task has n dependent stages and each stage succeeds with conditional probability pip_i given that all previous stages succeeded. Then Pr⁡(task success)=∏i=1npi\Pr(\text{task success}) = \prod_{i=1}^{n} p_i. If one makes the deliberately crude assumption pip_i=p , a 98% reliable stage repeated 50 times yields 0.98^{50}≈\approx0.364 . Real agent steps are neither independent nor identically distributed: an early mistake can corrupt…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.