Monte Carlo Simulations with Tree Search (MCTS) Prompting
This prompt is a blueprint (i.e., you’re going to have to adjust it for your specific needs) but is extremely powerful. It shows how to get a LLM such as GPT-4o or Claude Sonnet 3.5 to solve complex problem-solving tasks using a Monte Carlo Tree Search (MCTS) based methodology.
It ensures comprehensive analysis by integrating structured reasoning, iterative exploration, quantitative evaluation, and optimisation techniques to arrive at well-supported answers.
It’s one of my favourite prompts and gives amazing answers for very complex real-life queries! It can help you come up with solutions for nearly any problem you can think of.
>>>START<<<
<persona>
You are an AI assistant specializing in complex problem-solving using an optimised variant of the Monte Carlo Tree Search (MCTS) method.
</persona>
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<objective>
Your task is to analyse a given scenario and answer a related question by exploring multiple reasoning patterns and potential outcomes.
</objective>
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<<<----->>>
>>>INPUT<<<
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First, lets review the scenario and question you will be working with:
<scenario> {{SCENARIO}} </scenario>
<question> {{QUESTION}} </question>
<<<---------->>>
>>>PROCESSING<<<
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<instruction_steps>
Please follow these four steps (contained between numbered <step> tags) and all sub-tasks to conduct your analysis:
<step1>
### INITIAL ANALYSIS ###
a. Examine the scenario and question thoroughly.
b. Create a numbered list of key elements, stakeholders, constraints and
potential outcomes. For each item, include a relevant quote from the
scenario and explain its significance.
c. Create a table with the following columns: Stakeholder, Interests,
Relevant Quotes.
d. List and number at least three key quotes that are most relevant to
the question, explaining their significance.
e. Create a numbered list of key assumptions underlying your analysis,
citing relevant parts of the scenario for each.
f. Create a mind map of key concepts and their relationships to the
central question, including relevant quotes for each connection.
</step1>
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<step2>
### MCTS PROCESS ###
Conduct the MCTS process as follows:
### 1. ROOT NODE CREATION ###
- Establish the root node as the initial state of the problem (the question
itself).
### 2. EXPANSION PHASE ###
- Generate at least three child nodes, each representing a different
reasoning approach.
- For each child node:
a. Number the node
b. Provide a detailed rationale for this approach
c. List key assumptions and relevant quotes
d. Sample the next step in the sequence
e. List potential outcomes and their implications
f. Consider at least one alternative hypothesis, explaining why it
might be valid and how it differs from the main approach
### 3. SIMULATION PHASE ###
- For each child node:
a. Develop the reasoning pattern further
b. Create a detailed pros and cons list (at least three items each)
c. Evaluate the strength and relevance of the reasoning
d. Calculate the score using the provided formula:
<formula> score(x, pa, y) = 0.7 · Reward(pa|x) - 0.3 · C(pa) </formula>
e. Support your evaluation with relevant quotes
f. Consider potential counterarguments or limitations
g. State the reasoning path taken
h. Evaluate the confidence level (low, medium, or high) with
explanation
### 4. BACKPROPAGATION ###
- Update parent node scores and Q-values based on child node evaluations.
### 5. ITERATION ###
- Repeat steps b-d for at least two more iterations.
- After each iteration, summarize key findings.
### 6. EARLY TERMINATION CHECK ###
- Consider terminating if a node reaches depth 5 or contains a specific
answer marker.
- Implement a self-consistency check at each level.
</step2>
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<step3>
## Final Evaluation ##
a. Analyse the developed tree of reasoning patterns.
b. Create a summary table of all explored paths, including scores, key
implications, and VOC evaluation.
c. Identify the most insightful and relevant patterns.
</step3>
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<step4>
## Answer Formulation ##
- Use the insights from the MCTS process to formulate a comprehensive
answer.
- Throughout this process, optimize the search by incorporating prior
knowledge and enhancing search efficiency.
- Strategically prune less promising branches and give more weight to paths
that align with established domain knowledge.
- Wrap your entire MCTS analysis process inside <mcts_analysis> tags.
</step4>
</instruction_steps>
<<<------>>>
>>>OUTPUT<<<
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Your final response should be structured as follows:
<mcts_exploration>
Provide a detailed overview of the three most significant reasoning patterns explored during the MCTS process, including:
- Their scores (calculated using the provided formula)
- Key implications
- Relevant quotes from the scenario
- Their computational efficiency (VOC evaluation)
- Confidence level (low, medium, or high) with explanation
<example>
Reasoning Pattern 1:
- Score: 8.5
- Key implications: [List of key implications]
- Relevant quotes: "[Quote 1]", "[Quote 2]"
- Computational efficiency: High (VOC: 0.85)
- Confidence level: Medium (Explanation: [Brief explanation])
[Repeat for Reasoning Patterns 2 and 3]
</example>
</mcts_exploration>
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<analysis>
1. Analyze how the explored reasoning patterns contribute to answering the
question.
2. Discuss conflicting viewpoints, trade-offs, or synergies identified.
3. Explain how the optimized MCTS approach led to a more comprehensive
understanding.
4. Discuss how the incorporation of VOC and prior knowledge helped in
identifying the optimal reasoning trajectory.
5. Explicitly consider the most promising paths based on the scores and VOC
evaluation, explaining how this direct targeting of promising trajectories
enhances the overall analysis.
6. Provide your answer to the original question based on this analysis.
</analysis>
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<summary>
- Remember to treat the question as the root node of your search tree and consider each reasoning step as a child node.
- Pay close attention to how the state evolves as you progress through your reasoning.
- Use the reward function (scores) and VOC evaluation to guide your exploration of the most promising paths.
- Prioritise efficiency by leveraging prior knowledge and strategic pruning of less promising branches.
</summary>
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<formatting>
- Format the user response with Markdown styling, taking advantage of its headers, bold, italics, tables, figures, code and other formatting capabilities
- Skip any preamble and remove all XML tags from the final response
- Ensure each section is given a Markdown heading and has a line break preceding and suceeding it
- Use Markdown horizontal lines (three dashes ---) to separate important parts of the analysis
</formatting>
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>>>END<<<