Monte Carlo Simulator Runner

Execute comprehensive Monte Carlo simulations with configurable probability distributions, correlation modeling, and advanced statistical analysis for risk-quantified decision-making.

When to Use This Command

Run this command when...

• You need to quantify uncertainty in financial projections, project timelines, or capacity estimates with statistically rigorous confidence intervals
• You want to understand the full distribution of possible outcomes rather than relying on single-point estimates
• Your risk analysis requires sensitivity identification to determine which variables drive the most outcome variability

Do NOT use this command when...

• Your analysis has no meaningful uncertainty -- deterministic calculations are faster and clearer
• You need a quick back-of-envelope estimate rather than a full probabilistic analysis

Quick Start

Copy
# .claude/commands/monte-carlo-simulator-runner.md
# Run Monte Carlo simulation
Simulate: $ARGUMENTS

Copy
# Run the command
claude "monte-carlo-simulator-runner project completion timeline with 5 work streams, each 2-8 weeks duration"

Expected output:
- Distribution of total project duration (P10, P50, P90)
- Tornado chart identifying highest-impact variables
- Correlation effects between work streams
- Risk-adjusted timeline recommendation
- Confidence interval for stakeholder communication

Core Concepts

Concept	Description
Random Sampling	Generating thousands of scenarios by drawing from input distributions
Probability Distribution	Statistical shape (normal, triangular, uniform) assigned to each variable
Correlation Matrix	Models how input variables move together, preventing unrealistic combinations
Convergence	Point at which adding more iterations does not change the output distribution
Sensitivity Ranking	Orders input variables by their contribution to output variance

Monte Carlo Execution Flow:

  Define Variables & Distributions
       |
  [Set Correlations]
       |
  [Run N Iterations]
       |
  +----+----+----+
  |    |    |    |
  i=1  i=2  ... i=N
  |    |    |    |
  [Aggregate Results]
       |
  +----+----+
  |         |
 Output   Sensitivity
 Distrib.  Analysis
  |         |
  Percentiles & CI

Configuration

Parameter	Default	Description
Iterations	10,000	Number of simulation runs for statistical convergence
Distribution Type	Triangular	Default probability shape for uncertain inputs
Correlation	Independent	Whether to model correlations between input variables
Confidence Level	90%	Reporting threshold for confidence intervals
Output Metrics	P10/P50/P90	Percentile breakpoints reported in results

Best Practices

1. Specify distributions explicitly -- state "duration: 2-4-8 weeks (min-likely-max)" rather than "2-8 weeks" so triangular distributions are properly shaped
2. Declare correlations -- if two variables are linked (e.g., scope and duration), mention their relationship to avoid underestimating tail risk
3. Start with fewer variables -- model the 3-5 most uncertain inputs first, then expand. Over-parameterized models obscure which variables actually matter
4. Use sensitivity output -- the tornado chart tells you where to invest in better estimates. Focus data-gathering on the top 2-3 drivers
5. Communicate percentiles not averages -- stakeholders need to understand P10 (optimistic), P50 (median), and P90 (conservative) rather than a single expected value

Common Issues

1. Results seem unrealistic at extremes -- check your distribution tails. Uniform distributions create too many extreme values; switch to triangular or normal
2. Output does not converge -- increase iteration count. If results still shift, your distributions may have very heavy tails that require 50k+ iterations
3. All variables show equal sensitivity -- your input ranges may be too similar. Review whether each variable's uncertainty range reflects real-world knowledge