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

Annotations already declare readOnlyHint=true, destructiveHint=false, openWorldHint=false, so safety is covered. The description adds value by disclosing the exact formula used, implying deterministic closed-form computation with no side effects, but says nothing about precision, numerical behavior, or output shape (though an output schema exists).

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?

Two dense, front-loaded fragments with zero filler. The telegraphic style ('Binomial P(X=k), at_most, or at_least') is slightly awkward to parse but never wastes words.

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?

Given a fully documented schema, an existing output schema, and read-only annotations, the description covers what remains the tool's job: identifying the computation and formula. Only the mapping of mode semantics to results is left to inference.

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?

Schema description coverage is 100% with constraints (0<=k<=n, n>=0, p in 0..1) and a defaulted enum for mode, so the schema carries parameter meaning. The description only implicitly ties mode values to the three named cases; it adds no syntax or edge-case detail beyond the schema.

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?

States the specific verb/resource (binomial probability) and names the three supported modes plus the closed-form PMF, so the agent knows exactly what is computed. It does not differentiate from close siblings such as calculator_probability, calculator_normal, or calculator_random_distribution.

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?

No statement of when to use this versus alternatives; the mode enumeration (exact, at_most, at_least) merely restates what the schema's mode enum already provides. An agent must guess that this tool serves repeated-trial probability rather than general probability.

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