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

No annotations are provided, so the description must carry the full behavioral burden, and it provides nothing. It doesn't state determinism, edge-case handling (e.g., k > n), output format, or that the parameters k and n are typed as strings despite representing integers.

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 three words long and merely echoes the name, providing no concise framing or structure. Brevity is not the virtue here; it is under-specification.

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 no annotations, no output schema, and a mutation-ambiguous numeric computation, the description is completely insufficient. An agent cannot know whether this returns a count, a list, or an error for invalid inputs.

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 coverage is 100%, so the schema documents both params, giving a baseline of 3. The description adds nothing about the meanings of n and k or that they should be numeric strings, but the schema does the minimum.

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 is the tautological restatement 'Combination Count: Combination Count', adding no verb, resource, or scope beyond the name. Only the name hints at computing C(n,k) combinations, which is vague and not differentiated from siblings like x402-combinations, x402-binomial-coefficient, or x402-permutation-count.

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 indication of when to use this tool versus alternatives. No alternatives are named and no context is provided, leaving the agent to infer purely from the name in a namespace of hundreds of similar math tools.

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