Monte Carlo Simulation Playground
Overview
The Monte Carlo Simulation Playground lets you build and explore Monte Carlo simulations for various probability problems. Monte Carlo methods use repeated random sampling to obtain numerical results and estimate probabilities that might be difficult to calculate analytically. This interactive tool includes classic examples like estimating π, the birthday paradox, and the Monty Hall problem, plus a custom simulation builder for your own scenarios.
Tips
- Monte Carlo simulations approximate probabilities through random sampling (Law of Large Numbers)
- More iterations = more accurate estimates (but diminishing returns after ~100,000)
- Watch the convergence plot to see the estimate stabilize over iterations
- Compare simulated vs theoretical probabilities when known
- Confidence intervals narrow as sample size increases
- Classic problems: π estimation uses random points in a square, birthday paradox shows counter-intuitive probabilities
- Monty Hall demonstrates the value of switching doors (2/3 vs 1/3 probability)
- Use simulations to validate analytical solutions or explore complex scenarios
- The empirical distribution shows the actual outcomes from your simulation
- Standard error: SE ≈ √[p(1-p)/n] for proportion estimates