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

No annotations are provided, so the description carries the full burden and does so reasonably: it discloses the hard failure mode (400 below 20 values), the statistical caveat that small samples lack discriminating power, and states what it returns (p-value plus its own limitations). It doesn't cover auth or rate limits, but for a pure computation tool the key behavioral traits are surfaced.

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?

Purpose and constraints are front-loaded and dense, but roughly a third of the text is meta-commentary about the description's own authoring history ('the first version missed this line, I hit it myself'), which describes the definition rather than the tool and does not earn its place.

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?

With no output schema and no annotations, the description adequately covers the return value (p-value), the input floor (n>=20), the error behavior, and the interpretation caveat. An agent has enough to call it correctly and interpret the result reasonably.

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 100%, so `values` and `bins` are already fully documented in the schema. The description only restates the 20-value minimum and the 0/1-or-integer range, adding no format or syntax detail beyond the schema. Baseline 3 applies when the schema does the work.

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: runs a randomness check (chi-square + runs test) on 0/1 or integer sequences and returns a p-value. It also scopes itself against the obvious sibling (`lottery_draws`, `challenge_forecast`) by declaring it makes no lottery predictions, so an agent can separate it without opening the schema.

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?

Gives clear usage conditions: use on sequences of at least 20 numbers, treat n<100 results as weak, and do not use it for lottery prediction. It lacks explicit routing to a named alternative sibling, which keeps it from a 5.

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