Choose 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% intervals for binary outcomes, tracks convergence, and records each calculation step.
For handouts, export raw counts as CSV or copy the LaTeX summary. Use the shareable URL to reopen the same scenario later.
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?
Use a published acceptance case, such as seed 12345 with 100 flips. The simulator returns the same outcome each time because RNG and seed are fixed, even across devices.
Can I export the run to share with students?
Yes. Export CSV for raw counts and running estimates, copy the LaTeX summary for worksheets, and share the generated URL to reload the same experiment.