collision_probability

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

With no annotations, the description carries the full burden. It discloses the exact formula and example outputs, making the deterministic computational behavior transparent. It does not mention edge cases (e.g., zero items) or that it uses floating-point approximation, but the core behavior is well disclosed.

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?

The description is compact: a formula, two examples, and a practical note. It is front-loaded with the core formula and all sentences add value, with no fluff or repetition of schema 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?

Given the simple two-parameter calculator and the presence of an output schema (not shown but noted), the description adequately covers purpose, formula, and usage. Minor omissions like explicit return-type or edge-case behavior prevent a 5, but it is complete enough for typical use.

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 explain the parameters. It does so implicitly via the formula (n and b) and explicitly through examples ('1e6 items into 64 bits'). Both 'items' and 'bits' are clearly mapped, exceeding baseline for two-parameter tools.

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 clearly states the tool computes 'Birthday-bound hash collision probability' with a specific formula, distinguishing it from sibling tools like bit_analysis or data_sizes. The examples ('1e6 items into 64 bits is ~2.7e-8') reinforce the concrete purpose.

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 gives a concrete use case: answering 'can I truncate this to 8 hex chars?' and shows example scenarios. It does not explicitly name alternative tools for when not to use it, but the context is clear enough for an agent to select this tool for collision probability estimation.

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