binomial_probability

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Since no annotations are present, the description must disclose behavioral traits. It lists the allowed prob_type values and states that the return is a dictionary with probability and distribution info, but it does not explain the exact keys, edge-case handling, or what 'distribution info' includes. This leaves significant ambiguity about the tool's behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and well-structured, with a clear purpose line followed by a labeled Args section and a Returns section. Every sentence adds value with no redundancy, making it easy to scan.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Without annotations or an output schema, the description is the sole source of context. It covers the parameters and return type at a high level, but it does not specify the exact return structure, the meaning of each prob_type (e.g., cumulative = P(X≤k)), or error behavior. This is a minimum-viable description, but not a complete one.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has zero parameter descriptions, so the Args section must compensate. It does so by providing meaningful definitions for all four parameters: n as trials, k as successes, p as probability per trial, and prob_type with allowed values. However, constraints like p in [0,1] or k ≤ n are omitted, so it is not exhaustive.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description begins with 'Calculate binomial probability,' which clearly states the verb and resource, and it inherently distinguishes the tool from siblings like poisson_probability and normal_probability. The listing of key parameters (n, k, p, prob_type) reinforces the purpose.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no explicit guidance on when to use this tool versus alternatives, such as poisson_probability or normal_probability. It does not mention the conditions for a binomial distribution (e.g., fixed number of independent trials) nor exclude any alternatives. Usage is only implied by the function name and parameters.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.