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

No annotations exist, so the description carries the full behavioral burden. It discloses the x402 payment context (5 free trial calls per signed wallet), which is useful, but says nothing about parameter constraints (p in (0,1], k a positive trial count), return format, or error behavior for a 2-parameter computation tool.

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?

A single front-loaded sentence states the computation before the promotional addendum, with no wasted wording. The emoji/trial note is tangential but brief.

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 two-parameter math function with no output schema, the description covers the core meaning but omits domain constraints on p and k and any hint about the returned value. Adequate to attempt a call, incomplete for doing so reliably.

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% and both params are opaque strings, so the description must compensate. It does map the parameters semantically (k = point of evaluation, p = success probability), but gives no expected format, range, or validation rules for the string-typed values.

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 gives a specific verb (computes) and resource (geometric distribution probability mass at k for success probability p), which distinguishes it from sibling PMF tools like x402-binomial-pmf and x402-poisson-pmf. It stops short of explicitly routing between those siblings, but the mathematical object is unambiguous.

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?

There is no guidance on when to use this versus the other distribution tools (binomial-pmf, poisson-pmf, multinomial), nor any stated preconditions. The only extra sentence is a promotional note about free trial calls, which is not usage guidance.

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