Simulation CS Thinking Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA dice-rolling simulation generates random numbers 1-6 to simulate rolling a die 1000 times. Why might the simulated results differ from the theoretical probability (1/6 each)? What would make them converge?
Solution
- 1 Step 1: Random variation means small samples may not match theoretical probabilities exactly. In 1000 rolls, you might get 180 sixes instead of the expected 166.7 — this is normal statistical fluctuation.
- 2 Step 2: As the number of simulated rolls increases (10,000; 100,000; 1,000,000), the observed frequencies converge toward 1/6 each, by the law of large numbers.
- 3 Step 3: Additionally, computer random number generators are pseudorandom (deterministic algorithms), which could introduce subtle biases, though modern generators are extremely good.
Answer
Results differ due to random variation in small samples. They converge to theoretical probabilities as the number of trials increases (law of large numbers).
Monte Carlo simulations use random sampling to estimate results. Understanding that simulation results are estimates — not exact answers — and improve with more trials is critical for interpreting simulation output.
About Simulation
Using a computer program to model and experiment with a real-world system or process. Simulations represent key variables and their relationships mathematically, allowing you to test scenarios, make predictions, and explore outcomes without real-world cost or risk.
Learn more about Simulation →More Simulation Examples
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