This lab teaches probability as a practical reasoning problem, not a vocabulary quiz. It starts with a Monty Hall-style signal choice, then expands into guided presets for gambler's fallacy, hot-hand confusion, small samples, clustering, base rates, regression to the mean, outcome bias, and variance.
What the lab teaches: Probability work needs base rates, sample size, and patience with variance. The simulator makes it easier to see why a result can be surprising without being suspicious.
What to try first: Run the small-sample preset several times before changing any settings. Watch how often a short run looks like a story even when the underlying process has not changed.
Who it is for: Product builders, operators, analysts, students, and anyone reviewing noisy metrics, incident patterns, test results, or claims built from limited evidence.
Related research/project links: Pair this with Market Intelligence Field Notes for signal-vs-noise discipline and Chaos Divergence Explorer for systems where repeated feedback changes the shape of the outcome.
What this shows
Random does not always look random. A fair process can still produce streaks, clusters, and short runs that feel meaningful. The simulator shows the difference between the expected long-run tendency and the actual result from one local run.
How to read it
Each preset shows expected results beside actual results. Expected means what the rule predicts over many repetitions. Actual means what happened in this run. When those two are far apart, that gap is usually the lesson.
Every preset draws a real run rather than printing the closed-form answer, and nothing is seeded. The expected column is arithmetic you could do on paper; the lesson is the distance between it and one actual run, and that distance only exists if the run is really drawn. Leaving it unseeded is why the advice above is to run a preset several times — a repeatable number would start reading as the answer instead of as one draw.
Why it matters
Noisy systems show up everywhere: product metrics, alert queues, operations, hiring, quality control, weather, testing, and simple games of chance. The point is to avoid forcing a story onto a sample that is too small, too noisy, or missing the starting rate.
Limits
This is an educational probability lab. It is not a market model, investment recommendation, or proof that one move is always right in every real system. The presets are simplified models meant to clarify reasoning mistakes.
The simplification is deliberate in a specific way. In the regression-to-the-mean preset every batch is drawn from the same fair process, so none of them is genuinely better than another. The drop when the top performers are retested is therefore pure selection on noise — there is no skill anywhere in the model to explain it with, which is the only way to show the effect does not need one.
Related
Compare it with Chaos Divergence Explorer and Market Intelligence Field Notes.