What is Monte Carlo Simulation?

Monte Carlo simulation involves running many random experiments to estimate numerical results. It allows for “what-if” analyses, helping us understand potential outcomes by testing various scenarios based on random inputs. This method is widely used for risk analysis, from financial forecasting to engineering reliability.

Monte Carlo Simulation in Action: Rolling Dice Example

Example: Rolling two dice to calculate the probability of their sum being seven.

• Manual Calculation: There are 6 combinations out of 36 that sum to seven (Probability = 6/36 or 0.167).
• Monte Carlo Approach: Simulate rolling the dice 10,000 times, record the sum of each roll, and determine how often the sum equals seven. As simulations increase, the result will converge to the true probability (0.167).

This approach demonstrates how MCS can approximate probabilities through random sampling.

How Monte Carlo Simulation Works?

1. Determine Input Ranges: Define possible input values using historical data or expert knowledge (e.g., project completion times, investment returns).
2. Random Sampling: Use probability distributions (normal, uniform, triangular) to select random values for each input.
3. Run the Model: Execute the model with these inputs and record the results.
4. Repeat: Perform the simulation many times (often thousands) with different random values.
5. Analyze Results: Compile and analyze the results to understand the probabilities of various outcomes.

For more insights on the Monte Carlo Simulation, Read Our Article

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