Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple tool with one parameter, no output schema, and no annotations, the description covers the main things an agent needs: what the tool returns and when to use it. It could optionally describe the output format or behavior when no finished game exists, but the current description is sufficient for correct selection and invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.