Monte Carlo simulation explained for decision makers
The essentials in 30 seconds
- A Monte Carlo simulation returns a distribution of results, so a decision maker sees a range and the chance of missing a target.
- In the project cost example, the plan adds to 800 and the simulated average is about 893.
- A budget of 900 is overrun in about 45 percent of 10,000 trials, and a budget of 1,000 in about 10 percent.
- Materials show the strongest link to total cost, at about 0.78.
- The EQOS Asia deterministic core recomputes identically (EQOS Asia method page, as of October 2026).
A Monte Carlo simulation replaces one forecast with thousands of trial outcomes, so a decision maker sees a range and the chance of missing a target. This page explains how to read the result, using a project cost example with illustrative ranges, as of October 2026. The simulation was run for this page with 10,000 draws. It follows Monte Carlo simulation for decisions and focuses on interpretation.
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What does a Monte Carlo simulation tell a decision maker?
A plan gives one number, such as a cost of 800. A Monte Carlo simulation gives the whole picture: how the cost is spread across thousands of plausible cases, how likely the budget is to hold, and which inputs push the result around. The decision maker moves from asking whether the plan is right to asking how much room the plan needs.
The output is a distribution, usually shown as a histogram and summarised in a few numbers. Those numbers are the average, a handful of percentiles, and the probability of crossing a threshold such as the budget. Each answers a different question, and a good report states all of them.
What inputs does a Monte Carlo simulation need?
Three things are needed: a model that turns inputs into a result, a range for each uncertain input, and a number of draws. The model is often a spreadsheet formula. A range gives the lowest, the most likely, and the highest plausible value, and the draws repeat the calculation with random values taken from the ranges.
The ranges carry the judgement. They should come from past projects, supplier quotes, or expert views, with the source noted. A range invented to look reasonable produces a tidy result with no meaning. Spend the preparation time on the three or four inputs that move the result most.
What does a Monte Carlo simulation show for a project cost?
Take a project with three cost lines, all figures illustrative. Materials range from 300 to 600 with 400 most likely. Labour ranges from 250 to 450 with 300 most likely. Permits and other costs range from 80 to 200 with 100 most likely. The plan adds the most likely values and returns 800.
The simulation returns an average cost of about 893. The plan sits below the average because the ranges lean upward: each line can overrun much more than it can underrun. The gap of about 93 is the cost of skewed risk, and it is invisible in the single-point plan.
How do you read the percentiles of a Monte Carlo result?
A percentile gives the value below which a share of the trials fall. In the example, the 10th percentile is about 790, the 50th is about 890, and the 90th is about 1,000. Read this as follows: in 1 case out of 10 the cost stays under 790, and in 9 cases out of 10 it stays under 1,000.
The span from the 10th to the 90th percentile, about 210, describes the realistic range. A decision maker can pick the percentile that matches the appetite for risk. A cautious owner budgets at the 90th percentile, and an owner who accepts more risk budgets near the 50th and holds a reserve.
How do you read the chance of missing a target in a simulation?
Count the share of trials above the threshold. With a budget of 900, about 45 percent of the trials overrun. With a budget of 1,000, about 10 percent overrun. With a budget of 1,100, fewer than 1 percent do. The table of thresholds turns a vague worry into a statement the board can accept or reject.
The shift from 45 to 10 percent costs 100 in budget. Whether the extra 100 is worth it depends on the damage of an overrun and on the cost of holding the money back. The simulation does not make that call, and it frames the trade so that the owner makes it with open eyes.
Which assumptions move a Monte Carlo simulation result the most?
A sensitivity view ranks the inputs by their link to the result. In the example, the correlation with total cost is about 0.78 for materials, 0.53 for labour, and 0.32 for permits. Materials carry the widest range, so they explain most of the variation in the total.
The ranking directs effort. A fixed-price quote on materials narrows the largest range, and the chance of overrunning 900 falls accordingly. Time spent refining the permits estimate buys little, since that line has the smallest effect. Management attention then goes to the inputs that matter.
Which questions should a decision maker ask about a Monte Carlo result?
Five questions test the quality of a simulation. Where did each range come from? Are inputs that move together, such as materials and labour in a boom, linked in the model? How many draws were used, and did the answer stay stable across runs? Which inputs were left out? What does the result say about the decision itself?
A confident answer to each question makes the output trustworthy. If an analyst cannot say where a range came from, treat the result as a sketch. The method amplifies the quality of the inputs in both directions, and the questions expose that quality quickly.
How does the EQOS Asia decision engine differ from a Monte Carlo simulation?
Two runs of a Monte Carlo simulation with different seeds return slightly different figures. The EQOS Asia decision engine uses a deterministic core, the Codex Universalis, and every verdict can be recomputed identically (EQOS Asia method page, as of October 2026).
A reader can try a first score in the simulator on the same decision and place it beside the simulated range. The simulation shows how a result may spread, and the engine measures the structure of the situation on 9 dimensions.
See also in this guide
Frequently asked questions
What is a Monte Carlo simulation in simple terms?
A Monte Carlo simulation repeats a calculation thousands of times, each time drawing random values for the uncertain inputs from agreed ranges. The results form a distribution. It shows the average, the spread, and the chance of crossing a threshold, instead of a single number.
How do you read a Monte Carlo histogram?
The horizontal axis shows possible results and the vertical axis shows how often each occurred. Read the centre for the typical result, the width for the uncertainty, and the share to the right of a threshold for the chance of overrunning it. Compare percentiles with the plan.
What are P10, P50, and P90 in a simulation?
They are the 10th, 50th, and 90th percentiles. P10 is the value below which 10 percent of the trials fall, P50 is the median, and P90 is the value below which 90 percent fall. Together they describe the realistic range of the result.
Can the EQOS Asia pre-diagnostic follow a simulation?
Yes. The free 30-minute pre-diagnostic applies the EQOS Asia equation to the same decision across 9 dimensions and shows which carry the most risk. It runs by video in Singapore time (SGT) under NDA (EQOS Asia contact page, as of October 2026).
Test your knowledge
1. What does the plan add up to in the example?
- 893
- 800
- 1,000
Show the answer
800.
2. About how likely is an overrun of a budget of 900?
- 10 percent
- 45 percent
- 90 percent
Show the answer
45 percent.
3. Which input has the strongest link to total cost?
- Materials
- Labour
- Permits
Show the answer
Materials.
4. What does the 90th percentile of about 1,000 mean?
- 9 cases out of 10 stay under it
- The cost always reaches it
- 1 case out of 10 stays under it
Show the answer
9 cases out of 10 stay under it.
5. How many draws were used in the example?
- 100
- 1,000
- 10,000
Show the answer
10,000.
About the author
Stéphane Jambu
President, EQOS Forecast Asia
Stéphane Jambu leads EQOS Forecast Asia and works as a consultant in e-commerce, search visibility, and AI. LinkedIn profile
Sources: EQOS Asia method page (eqos-asia.com/method.html), simulator page (eqos-asia.com/simulator.html), and contact page (eqos-asia.com/contact.html), consulted on 22 October 2026. Page updated on 22 October 2026.