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

Annotations already declare the full safety profile (readOnly, idempotent, non-destructive, closed-world), so little behavioral disclosure is required. The description adds that it returns an 'odds_one_in' value and the underlying math model, but does not describe any behavioral traits beyond what annotations and the output schema already convey.

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 tight sentences with the core computation front-loaded. The trailing list_bundles cross-reference is marginally useful and does not bloat the definition, though it is not essential to calling the tool.

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 an output schema present, return values need not be explained, and annotations plus full schema coverage handle parameters and behavior. The remaining incompleteness is the lack of differentiation from similar probability siblings.

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%, so deck_size, draw_count, target_cards, and cards_in_deck_matching are all documented in the schema. The description adds no parameter-level meaning (e.g., the relationship between target_cards and cards_in_deck_matching), so baseline 3 applies.

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 ('Calculate hypergeometric probability of drawing specific cards from a deck'), and naming the hypergeometric model distinguishes it somewhat from generic probability siblings. However, it does not explicitly differentiate itself from closely related siblings such as calculate_poker_hand_probability or calculate_dice_probability.

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?

The only guidance is 'See list_bundles for related jeux-probabilites calculators,' which points to a catalog rather than explaining when to use this tool over the many probability siblings. There is no when-to-use, when-not, or alternative-tool routing for the actual decision an agent faces.

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