Choose among coin flips with custom p(Heads), weighted six-sided dice, or European/American roulette bets. The simulator compares theory and empirical ratios, shows Wilson 95% confidence intervals for binary outcomes, tracks running convergence, and records the exact steps it takes so you can explain them back to the class.
Need extra documentation? Use the CSV export for raw counts, the LaTeX summary for worksheets, and the shareable URL to resume the exact scenario in your next session.
Controls
Distribution (theory vs empirical)
Blue bars track empirical frequencies while the lighter overlay shows theoretical probabilities. Differences are labeled above each category for quick reference.
Running estimate vs trials
The solid line shows the running proportion. The dashed line marks the theoretical value and the shaded band gives the 95% confidence interval as trials accumulate.
Teaching tips
- Demonstrate the law of large numbers by increasing trials and letting learners watch the convergence band tighten around the theoretical line.
- Switch the dice to weighted mode and discuss how expected frequencies change and how the χ² statistic reacts to mis-specified weights.
- Highlight roulette's expected value and house edge to connect probability with finance-style expected returns.
FAQ
How can I verify the RNG sequence in class?
Pick the published acceptance cases—e.g., seed 12345, 100 coin flips—then show how the simulator reports 44 heads every time. Switching devices yields the same outcome because the RNG and seed are fixed.
Can I export the run to share with students?
Yes. Use CSV for raw counts and running estimates, copy the LaTeX summary for worksheets, and share the auto-generated URL to reload the same experiment later.