collision_probability

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

With no annotations, the description carries full disclosure burden. It reveals the underlying formula (1 - exp(-n^2/(2*2^b))) and provides example outputs, which is transparent about the computation. However, it does not mention what the function returns (decimal, percentage, rounding), possible edge cases (items=0, bits=0), or that it's an approximation (it uses exp). This is adequate but not exhaustive.

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 and front-loaded with the formula, then provides two illustrative examples and a practical takeaway. Every sentence earns its place, and the structure is clear. Slightly more formatting (like parameter definitions) could improve scannability, but it's already quite efficient.

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 tool is a simple calculation with only two numeric inputs and no output schema, the description is complete. It explains the purpose, gives the mathematical formula, provides example sizes with results to build intuition, and ties it to a real-world question. No additional context is needed for an agent to invoke it correctly.

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?

The schema provides no descriptions for 'items' and 'bits' (0% coverage), so the description must compensate. It does so by explaining that items is the number of items and bits is the hash size in bits, and gives concrete examples (1e6 items into 64 bits, 1e5 into 32 bits) that illustrate their meaning. This adds meaning well beyond the bare 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?

The description clearly states the tool computes birthday-bound hash collision probability and provides the formula. It distinguishes itself from sibling tools by being the only one focused on collision probability, and gives a concrete use case ('can I truncate this to 8 hex chars?'). This is a specific verb+resource with clear 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 implies when to use it: when you need to assess collision risk when truncating hashes, supported by numerical examples. It does not explicitly exclude alternatives or compare to other calculation tools, but the examples and phrasing give clear contextual guidance. A slightly more explicit 'use this when...' statement would push it to 5.

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