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

With no annotations, the description carries the full behavioral burden. It does disclose what is returned (the probability mass) and reveals a lifecycle constraint not present in structured fields (5 free trial calls per signed wallet), which implies wallet signing is required. It stops short of stating numeric domain constraints (lambda > 0, k non-negative integer) or error behavior.

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 with the core operation front-loaded. The trailing trial-offer clause is promotional rather than functional, but it is brief and does convey a usage constraint, so it is not pure waste.

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 simple two-parameter deterministic math function with no output schema, the description is nearly callable as-is. The gaps are the unspecified input format for string-typed numerics and the absence of domain constraints, both of which matter given 0% schema coverage.

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 0%, so the description is the only source of parameter meaning. It does map both parameters semantically ('at k for a given lambda'), which is more than the bare schema offers. However, it never addresses the odd string typing of k and lambda, so an agent has no guidance on accepted input format.

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 and resource: 'Returns the Poisson probability mass at k for a given lambda.' An agent can identify the operation, and the 'Poisson' qualifier distinguishes it from the many sibling distribution tools (x402-binomial-pmf, x402-geometric-pmf). It does not, however, explicitly route the agent away from those siblings.

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 when-to-use or when-not-to-use guidance, and no mention of the sibling distribution functions it could be confused with. The only 'context' offered is a promotional line about free trial calls, which does not help the agent decide whether this tool is the right one.

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