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

No annotations are supplied, so the description carries the full burden. It does disclose a real behavioral trait beyond the schema: the tool is metered/paid, with 5 free calls per signed wallet — useful for an agent managing cost. It says nothing about how invalid inputs (k > n, negative values) are handled or the response shape, leaving the core behavioral picture incomplete.

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?

One sentence, front-loaded with the definition before the commercial note. Nothing is redundant. Slightly terse given the undocumented parameters, but well-formed.

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?

For a trivial two-input math helper with no output schema and no annotations, the minimum needed is: what is computed (present), parameter roles (implied), and result form (absent). The formula plus pricing note makes it callable, but a fully complete definition would state the return type and the ordering/limits of n and k.

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 0%, so the description must compensate. It does convey the roles of the two parameters ('k-permutations of n items' implies n = pool size, k = selection size), which is more than the bare 'k'/'n' names offer. It leaves the string type and acceptable formats (e.g. huge n for big-integer math) unexplained, so it only partly fills the gap.

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 a specific operation and its mathematical meaning: 'Returns nPk, the number of k-permutations of n items.' An agent knows exactly what value is computed. It does not, however, distinguish itself from the sibling x402-permutations or x402-combination-count, so the sibling-differentiation criterion for a 5 is unmet.

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?

There is no statement of when to use this tool versus x402-permutations (which presumably enumerates them) or x402-combination-count. The only context given is commercial ('5 free trial calls per signed wallet'), which says nothing about tool selection. The agent must infer usage from the name alone.

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