Mcts

Use the MCP tool mcts_init_tree to initialize the search tree.

Phase 2: MCTS Loop (repeat until solution found or budget exhausted)

Execute the four MCTS phases in order:

2.1 Selection (UCB1)

Use /mcts:mcts-select skill or mcts_select MCP tool to:

• Traverse from root using UCB1: UCB = Q/N + c * sqrt(ln(parent_N) / N)
• Balance exploitation (high Q/N) vs exploration (low N)
• Select the most promising leaf node

2.2 Expansion

Use /mcts:mcts-expand skill or mcts_expand MCP tool to:

• Generate possible actions from selected node
• Use LLM as world model to predict plausible next states
• Add new child nodes to the tree

2.3 Simulation (Rollout)

Use /mcts:mcts-simulate skill or mcts_simulate MCP tool to:

• From expanded node, simulate to terminal state
• Use LLM as policy to guide simulation
• Evaluate the outcome (success/failure/partial)

2.4 Backpropagation

Use /mcts:mcts-backpropagate skill or mcts_backpropagate MCP tool to:

• Update statistics from simulated node to root
• Increment visit counts (N)
• Update value estimates (Q)

Phase 3: Solution Extraction

After sufficient iterations:

1. Use mcts_get_best_path to extract the best solution path
2. Present the solution with confidence scores
3. Explain the reasoning chain

Beliefs and Observations

Throughout the search:

• Use mcts_add_observation to record what you learn
• Use mcts_update_belief to update probability estimates
• Use mcts_get_beliefs to check current understanding

Prompt Dataset

Access reusable prompts with:

• mcts_dataset_list - View available prompts
• mcts_dataset_get - Retrieve a specific prompt
• Use /mcts:mcts-dataset for full CRUD operations

Execution Strategy

1. Start with a reasonable iteration budget (e.g., 10-50 iterations)
2. Monitor convergence - if best path stabilizes, can stop early
3. Use observations to refine the search space
4. Present intermediate progress for complex problems

Now execute MCTS for the given problem, using the appropriate MCP tools and skills.