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

Annotations already declare the tool as read-only, idempotent, non-destructive, and not open-world. The description adds that computation is 'exact' and inputs are 'bounded integers', which is useful behavioral context, but the bounds themselves are fully specified in the schema. No contradiction with annotations.

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?

A single, front-loaded sentence with no filler. Every word contributes to stating the operation and its input constraint.

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?

An output schema exists, so the description need not explain return values, and annotations cover the safety profile. The schema fully documents all three parameters. The main missing element is explicit usage guidance when choosing between combinations and permutations, but the mode enum partially covers that distinction.

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%, so the baseline is 3. The description's mention of 'nCr' and 'nPr' loosely maps to the mode enum, and 'bounded integer inputs' gestures at n and r, but it adds no meaning beyond what the schema already provides for each parameter.

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 gives a specific verb ('Compute') and resource ('combinations nCr or permutations nPr'), making the tool's operation unambiguous. It does not explicitly differentiate from any sibling tool, though none of the listed siblings perform combinatorial counting, so the lack of direct naming is minor.

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 description offers no when-to-use guidance, no when-not-to-use conditions, and no alternatives. It only states what the tool computes. For a calculator among many sibling calculators, it does not help the agent decide when this is the right tool versus, say, scientific_evaluate or power.

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