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

With no annotations, the description carries the full behavioral burden, and it discloses almost nothing: no return shape, no indication of whether the input is a starting value or a sequence, no error behavior. The one genuine addition is the payment clause (5 free trial calls per signed wallet), which tells the agent the call is metered against a wallet signature.

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?

It is short, but shortness here reflects under-specification rather than efficiency: the first clause is a redundant duplication of the name, and the only substantive sentence is an unrelated promotional note.

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?

A computational tool with two ambiguous undocumented parameters, no annotations, and no output schema leaves the agent with no way to call it correctly. The description should at minimum define the input number and the semantics of the returned length, and it supplies neither.

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% across two string parameters named "n" and "value", and the description says nothing to disambiguate them. An agent cannot tell whether these are aliases for the same starting integer, whether both must be supplied, or what format is expected. This is the most damaging gap in the definition.

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?

"Hailstone Length: Length of hailstone" is effectively a restatement of the tool name, repeating the same noun phrase twice rather than describing an action on a resource. It hints at the Collatz/hailstone domain but never states that it computes the number of steps in a hailstone sequence, nor does it distinguish itself from the sibling x402-hailstone-max.

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 when-to-use guidance, no prerequisites, and no reference to the near-identical sibling x402-hailstone-max or to x402-collatz. The only extra sentence concerns the free trial quota for signed wallets, which is billing context rather than usage guidance.

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