calculate_probability_binomial

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

No annotations provided, so description carries full burden. It does not disclose computational limits (though n max is in schema), edge cases, or side effects. It only lists return fields.

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 sentences, front-loaded with core purpose. Second sentence efficiently points to related resources. No wasted words.

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?

Given output schema exists, description provides return fields and hints at related tools. Lacks mention of constraints like n max or k <= n, but overall complete for a simple calculation tool.

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%, and description does not add extra meaning beyond what the schema already provides for n, k, p. Baseline of 3 applies.

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?

Description clearly states the tool calculates binomial probability P(X=k) and cumulative P(X<=k). It is specific but does not differentiate from siblings like calculate_dice_probability or calculate_card_draw_probability, though it hints at a category via list_bundles.

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?

No guidance on when to use this tool vs alternatives. It only mentions see list_bundles for related calculators, but does not provide explicit when/when-not criteria.

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