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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds real context beyond them: the exact output encoding (comma-separated), the n<=32 bound, the paid x402 pricing model, and an equivalent HTTPS endpoint. Nothing contradicts the annotations; the only gap is return size/pagination, which is bounded by n<=32.

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?

Front-loads the purpose, then the concrete example, then constraints, then pricing. Dense and mostly waste-free, though the pricing/URL sentence is boilerplate rather than tool semantics.

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?

With only 2 params, no output schema, and full annotation coverage, the description supplies the missing pieces an agent needs: what the output looks like, the hard bound on n, and the example that disambiguates 'moves'. Adequate for this complexity.

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 0%, so the description must carry the load. It clarifies n's meaning and range and demonstrates moves via the example set 1,2,3, but never states formally that 'moves' is the set of legal subtraction amounts or what the 1-100 element bounds imply.

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 computation and result: Grundy values from heap 0 through heap n for a subtraction game, returned comma-separated. It does not name or distinguish itself from siblings subtraction_grundy or subtraction_win, so an agent must infer that this returns a whole row rather than a single value.

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?

Usage is only implied by the worked example ('with moves 1, 2, and 3, the row through 8 is ...') and the n range. There is no explicit statement of when to pick this over subtraction_grundy (single value?) or subtraction_win (win/loss), which are the obvious alternatives.

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