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

Annotations already declare readOnlyHint, idempotentHint, non-destructive and closed-world, so the safety profile is covered. The description's only added content is the return-field list, which merely duplicates the existing output schema; it discloses nothing extra such as the n<=170 bound behavior, numeric precision, or error conditions.

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?

Two short sentences, front-loaded with the operation and its variants. The returns sentence is redundant with the output schema but costs little.

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?

Purpose is fully specified and the output schema means return values need no explanation. However, for a probability tool sitting among dozens of look-alike calculators, the absence of any when-to-use guidance leaves 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?

Schema description coverage is 100% (n, k, p each documented with ranges), so the baseline is 3. The formula notation implicitly maps k to successes and n to trials but adds no syntax, units, or constraint 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) plus the exact resource and formulas: binomial P(X=k) and cumulative P(X<=k). Naming 'binomial' distinguishes it from the many other probability siblings (dice, card draw, poker hand, lottery odds) without opening a 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?

The only routing sentence is 'See list_bundles for related education calculators,' which is a catalog pointer, not usage guidance. It never says when to pick this over calculate_dice_probability or calculate_lottery_odds, nor states any prerequisites.

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