combination_calc

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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false and openWorldHint, which fully characterize a pure deterministic calculation. The description adds no behavioral context such as edge-case handling (r > n, zero/negative values, fractional inputs), so it does the minimum beyond the structured data.

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 zero filler that names the operation, its notation, and its semantic character (unordered). Nothing could be removed without losing information.

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 two-parameter pure math function with fully documented params, rich safety annotations, and no output schema needed, the description is nearly sufficient. The only omission is edge-case/domain behavior for invalid inputs, which is a minor gap given the complete schema.

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% — n and r are both documented ('Total number of items', 'Number of items to choose') — so the baseline is 3. The C(n,r) notation in the description reinforces the mapping but adds no meaning beyond the schema.

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 verb (Calculate) and resource (number of combinations C(n,r)), and the qualifier 'unordered selections' semantically separates it from the ordered counterpart permutation_calc. An agent can identify the operation without opening the schema.

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: an agent infers it should call this when it needs C(n,r). There is no explicit when-to-use, no mention of permutation_calc as the alternative for ordered selections, and no stated preconditions (r <= n, non-negative integers).

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