Use this page when value per trial matters
Use Probability Simulator when you mainly need event frequencies, confidence intervals, or roulette-style outcome tracking. Use this page when the real question is “What do I expect to gain or lose on average per trial?”
If the setup already names a model such as binomial or Poisson, move next to Distributions for exact PMF/CDF and quantiles.
How to use
- Pick a preset that matches the situation you want to explain.
- Edit the values or probabilities if your own payoff table differs from the preset.
- Increase the number of trials until the running average settles near the theoretical target.
The top cards show the target and the observed average first. The chart then answers whether the gap is shrinking or still unstable.
Outcome table
| Outcome | Value | Probability |
|---|
How to read the result
Convergence chart
Outcome breakdown
FAQ
When should I use this instead of the probability simulator?
Use this page when you want to compare theoretical expected value and variance against repeated random trials. Use the probability simulator when you mainly care about event frequencies, confidence intervals, and per-outcome convergence for coin, dice, or roulette experiments.
Why does the simulated average not match the expected value exactly?
A simulation only approximates the long-run average. The gap shrinks as the number of trials grows, but short runs can still land above or below the theoretical target.
Can I edit the outcome values and probabilities?
Yes. Each preset loads a starting table, but you can change the labels, values, and probabilities before recalculating. Probabilities are normalized automatically as long as their total stays above zero.
What is the best next page after this one?
Move to the distributions page when the process already names a model such as binomial or Poisson. Move back to the probability simulator when you want to inspect event frequencies or confidence intervals instead of value per trial.