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

Annotations already declare readOnly/non-destructive, so the safety profile is covered. The description adds genuine behavioral context the annotations don't: the closed-form formula, the boundary behavior that lambda > 2 yields probability 1 rather than the raw formula value, and what is returned. It stops short of discussing numerical edge cases like alpha approaching 0/1.

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 reference and formula, then modes, then examples, then return values. Dense but every sentence carries information; the two illustrative examples are the only mildly redundant element against the mode description.

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?

No output schema exists, and the description compensates by explicitly listing the returns (probability, lambda_fraction echoed or solved) and disclosing boundary behavior. For a 3-parameter read-only calculator, an agent has everything needed to invoke it correctly.

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 baseline is 3. The description still adds value by framing the mutual exclusivity of lambda_fraction and max_probability as a mode switch, and by restating the (0, 2] validity bound that constrains the input beyond the schema's raw type descriptions.

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?

Names a specific computation (Kelly growth-security frontier probability) with an academic citation, and precisely states the two operating modes: compute probability from lambda_fraction, or solve lambda from max_probability. No sibling tool overlaps, so the agent can distinguish it purely from the description.

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 explicit selection logic ('Provide either lambda_fraction ... or max_probability ...') plus two natural-language user-phrasing examples that anchor real invocation intents. It also states the valid lambda range (0, 2], which is a usage constraint rather than just a domain fact.

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