Science collection
Statistics and simulation
Read data with the right denominator, measure uncertainty and separate exploration from prediction.
Start with Monte Carlo Simulation: Learn Probability by Repeating the Model, then follow the questions below. Each guide includes a worked explanation, a figure and routes to an experiment or calculator.
Statistics and simulation
Monte Carlo Simulation: Learn Probability by Repeating the Model
Build a trustworthy probability simulation with a defined event, reproducible generator, uncertainty estimate and exact benchmark where available.
3 min read · Formula & figureStatistics and simulation
Can Statistical Tests Prove Lottery Numbers Are Random?
Learn what frequency, runs and goodness-of-fit tests can detect, and why passing tests is not proof of fairness or unpredictability.
3 min read · Formula & figureStatistics and simulation
Expected vs Observed Lottery Frequencies: Reading a Table Properly
Learn expected counts, standard deviations and selection effects so a lottery frequency table describes data without pretending to predict the future.
3 min read · Formula & figureStatistics and simulation
Monte Carlo Error: Why a Million Trials Can Still Be Too Few
Estimate simulation precision, understand zero observed successes and distinguish absolute error from relative error for rare events.
3 min read · Formula & figureStatistics and simulation
Multiple Comparisons: Why Random Data Keeps Producing “Signals”
Calculate how repeated testing creates false alarms and learn why a pattern found after a broad search needs a different interpretation.
3 min read · Formula & figureStatistics and simulation
The Law of Large Numbers Does Not Make a Losing Number Due
See how sample proportions stabilize without future compensation, and why absolute deviations can grow while relative errors shrink.
3 min read · Formula & figureStatistics and simulation
Why Lottery Backtesting Can Fool You
Spot overfitting, test-set reuse and future leakage, and learn what a fair prospective evaluation of a lottery selection rule would require.
3 min read · Formula & figure