Ten million 6/49 draws: how uneven does fair look?

What happened

The lowest count was 1,221,974 and the highest was 1,227,407, around a common expectation of 1,224,489.796. At least one adjacent pair appeared in 49.49696% of draws.

The spread is the subject of the experiment, not a ranking to use next time. Every simulated draw used the same label probabilities. The most extreme labels were identified after all 49 counts had been inspected. Their extremeness should not be evaluated as if they had been specified before the run.

Method and benchmark

10,000,000 independent uniform six-number subsets of 1–49. Count every inclusion; compare with N × 6/49. The CSV contains all 49 sufficient frequency totals, not the raw draws.

For a fixed label, X has a binomial marginal distribution with p=6/49 and N=10,000,000. The sum of all counts is exactly 60,000,000. This provides a strong conservation check. The labels’ counts are dependent because each draw contains exactly six selections.

What this does not establish

A simulated fair process cannot certify a real lottery. Individual counts are binomial; counts for different numbers are dependent. The maximum is selected after inspecting 49 counts.

The downloadable CSV contains all 49 aggregate counts and their expectations. It does not contain ten million raw lines. The published seed and program regenerate those lines and the reported totals. This compact representation is sufficient to rebuild the frequency figure.

These are original educational simulations prepared for RoomForChance. They are not historical lottery records, a physical-machine audit, an external peer review or evidence of a prediction advantage.

Inspect the data

Download ten-million-649-draws.csv · All results and metadata (JSON) · Download the complete Python program · Download figure-generation code

Reproduce the experiment

Download the Python program to an empty working folder. Use the recorded environment for an exact replay. The program runs all eleven studies and creates a lab-data folder containing the result files. The largest study performs ten million draws; allow time for it to finish.

python -m pip install numpy==2.3.5
python run_experiments.py

Expected CSV SHA-256: 6f7cc9bcd5f49fdfdc25ae10f64180ae8b767b85e365ae7b28678dd21229aba9. A matching seed alone is insufficient if you change the implementation or call sequence. The CSV files use CC BY 4.0; the original code uses the MIT license included with the downloads.

Read the reasoning

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