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Kuhn poker equilibrium (CFR+)

solve_equilibrium
Read-onlyIdempotent

Solve Kuhn poker with CFR+ self-play, measure exploitability with pure best responses and compare the game value with -1/18. Illustrative game theory, not gambling advice.

Tool call template

This tool declares no required parameters. Add optional parameters from the input schema as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {},
    "name": "solve_equilibrium"
  }
}

Input Schema

NameRequiredDescriptionDefault
iterationsNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A3.6/5.0
Behavior3/5

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

Annotations already declare readOnly, idempotent, non-destructive, closed-world behavior, so the safety profile is covered. The description adds genuine value by disclosing the algorithm and the reported metrics, but it says nothing about runtime cost at the 200k default, convergence behavior, or how iterations trade off against accuracy — material for a tool whose only knob is a compute budget.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two sentences, front-loaded with the action and method, followed by the reported results and a scoping disclaimer. Nothing is padded and the disclaimer is short enough to justify itself for a poker-themed tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description does useful work by naming the returned measures (exploitability, game-value comparison). However, for a simulation whose sole input controls accuracy and cost, the absence of any guidance on iteration counts or expected compute time leaves a real gap for an agent deciding how to invoke it.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0% and the single parameter (iterations) is never mentioned in the description. The schema supplies default, min, and max, so the agent can technically call it, but nothing explains what raising or lowering iterations does to convergence or exploitability — the one piece of semantics an agent actually needs here.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description names a specific verb and resource ("solve Kuhn poker") plus the method (CFR+ self-play) and what it reports (exploitability via pure best responses, game-value comparison against -1/18). No sibling tool overlaps this problem domain, so the agent can place it unambiguously.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is only implied: the description makes clear this is a self-contained solver for one specific game, and the disclaimer "Illustrative game theory, not gambling advice" scopes it. There is no explicit statement of when to reach for this versus another analysis tool, and no note on when a higher iteration count is warranted.

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

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