Why this matters
A model is only useful once you run it. Pour water into a virtual tank, let a savings account grow for ten years in seconds, or throw thousands of random darts to estimate pi. A simulation lets you predict what would happen without waiting for, or risking, the real event.
The idea
A simulation means operating a model to predict an outcome. Spreadsheets make this easy, and the kind of model decides how you run it.
Deterministic simulations just apply a fixed formula row by row. Pour water at 6 L/min and water
volume = inflow rate times elapsed time, so fill the elapsed-time column and copy the formula down. For
savings under compound interest, each year's interest = balance times rate, and the next
balance = balance + interest, so each row feeds the next. To keep a copied formula pointing at the
fixed rate cell you use an absolute reference ($B$3); a relative reference (C3) instead
shifts as you copy.
Probabilistic simulations need randomness, supplied by the RAND function (a random number between 0 and 1). The classic example is the Monte Carlo method: estimate pi by scattering random points in a 1-by-1 square and counting how many land inside a quarter circle of radius 1. The IF function tags each point inside (1) or outside (0), and pi is about 4 times the fraction inside. The more points you throw, the more accurate the estimate gets.
Picture it
flowchart TD S[Simulation: run a model to predict] --> DET[Deterministic model] S --> PRO[Probabilistic model] DET --> F[Apply a fixed formula, copy it down] PRO --> R[Use RAND for random numbers] R --> MC[Monte Carlo: count points inside, more points = more accurate]
Worked example
Estimate pi the Monte Carlo way. Suppose 1,000 random points are dropped in the square and 750 fall inside the quarter circle. The fraction inside is 750 / 1,000 = 0.75, and pi is about 4 times that: 0.75 times 4 = 3. Throw 10,000 points with 8,000 inside and you get 0.8 times 4 = 3.2. Same method, and with far more points the estimate keeps closing in on the true value of pi.
Your turn
Try the practice questions. Decide which models are deterministic vs probabilistic, and match each spreadsheet tool (RAND, IF, absolute reference, Monte Carlo) to its job.
Recap
- A simulation runs a model to predict an outcome.
- Deterministic runs apply a fixed formula; use absolute references (
$) for cells that must stay fixed when copied. - Probabilistic runs use RAND; the Monte Carlo method estimates values like pi, and accuracy grows with the number of random points.