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

No annotations are provided, so the description carries the full disclosure burden. It usefully reveals the auth/quota model (signed wallet, 5 free trial calls) and the algorithm used, which is more than nothing, but it says nothing about valid input ranges for large n, failure behavior, or the shape of the result.

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?

It is front-loaded and short, but the 'Derangement Count:' prefix merely restates the name and the emoji trial blurb is marketing filler relative to the tool's function.

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 one-parameter math utility with no output schema and no annotations, the description covers the core purpose and payment model. It still omits the expected input format/limits and the return shape, which for a schema that types the input as a string is a real gap.

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 single parameter has 0% schema description coverage, so the description must compensate. It only says 'an integer n', which is vague and arguably conflicts with the schema's `"type": "string"`, giving an agent no reliable format, range, or sizing guidance.

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?

It states a specific verb and resource ('Computes the number of derangements for an integer n') and even names the algorithm (subfactorial recurrence), so the purpose is unmistakable and distinct from siblings like x402-permutation-count or x402-factorial-series. It does not, however, explicitly contrast itself with any alternative tool.

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 only guidance is a pricing note ('5 free trial calls per signed wallet'), which is not usage guidance. There is no statement of when to prefer this tool over related counting tools, nor any when-not condition.

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