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

Annotations already declare readOnly, idempotent, non-destructive behavior, so the bar is lower; the description still adds real operational context that no annotation carries — the $0.001 USDC per-successful-call x402/Solana payment model and an equivalent HTTPS endpoint (POST /api/x402/v1/josephus-first). What it omits is the return shape, i.e. whether the eliminated person is returned as a 1-indexed position or a remaining-person label.

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?

Front-loaded with the definition, then two worked examples, then bounds, then pricing and the HTTPS alternative — each sentence adds a distinct piece of information with no repetition. Two examples used to pin down k is justified given the 0% schema coverage.

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-integer, side-effect-free computation with rich annotations and no output schema, the description supplies essentially everything needed to call it correctly: domain bounds, interpretation of both parameters via example, cost, and a transport alternative. The only gap is the exact form of the returned value and what happens at the n=1 boundary (stated as having nobody to eliminate, but not as an error vs. a defined result).

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 must carry parameter meaning. It does bind the names to bounds ('n runs from 2 to 10000 and k from 1 to 10000') and the examples implicitly define n as the circle size and k as the counting step, but the semantics are conveyed only by example rather than stated directly.

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 states a specific verb+resource relationship: 'The first person eliminated in the Josephus circle,' making the computed quantity unambiguous. It does not, however, distinguish itself from close siblings such as josephus_place, josephus_order, or josephus_k2, which an agent would need in order to be confident this is the right variant.

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?

Usage is only implied — the definition and worked examples let an agent infer the applicable domain (n>=2 rotation with step k). There is no explicit statement of when to prefer this over josephus_place or josephus_order, nor any exclusion such as the degenerate single-person case, which is mentioned only as trivia rather than as a guard.

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