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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so safety is covered. The description adds genuinely useful model semantics: the independent single-box assumption and the caveat that sealed whole-case allocation can produce different results. That is context beyond what annotations provide.

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?

Two sentences, no filler, with the primary output (pull probability) front-loaded before the secondary outputs and caveat. The em-dash caveat is information-dense but earns 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?

There is no output schema, and the description compensates by naming the returns: the probability plus the 50% and 90% box counts. Combined with the model caveat, an agent has enough to invoke and interpret the tool correctly, though the sibling relationship remains unaddressed.

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 100% and both parameters carry examples ('e.g. 12', 'e.g. 72'), so the schema does the heavy lifting. The description repeats the 1-in-oddsN and N semantics without adding format or edge-case detail beyond the schema.

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 precise computation: probability of at least one secret in N blind boxes at 1-in-oddsN odds, plus the box counts for 50% and 90% thresholds. That is specific verb+resource+scope. It never names the close sibling calculate_style_probability, so the agent must infer the distinction from the word 'secret' alone.

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?

It gives a validity condition ('Independent single-box model — sealed whole-case allocation can differ') rather than when-to-use guidance. No explicit routing to or away from alternatives such as calculate_style_probability is provided, so usage is only implied.

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