Room for ChanceThe science of chance

RoomForChance Lab

Don’t just trust the claim.
Inspect the experiment.

Eleven original studies with executed results, explicit models and reproducible code. Every chart tells you what was measured—and what was not.

All 49 inclusion counts from 10,000,000 synthetic 6/49 draws, centered on N × 6/49 and scaled by the standard deviation for one prespecified label. The counts are dependent; this is not a simultaneous significance test.
Figure 1. All 49 inclusion counts from 10,000,000 synthetic 6/49 draws, centered on N × 6/49 and scaled by the standard deviation for one prespecified label. The counts are dependent; this is not a simultaneous significance test.

These are synthetic model studies, not historical lottery results. Use the exact benchmarks to understand the model, the data to inspect its variation and the source code to reproduce the run.

Experiment 01

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

10,000,000 independent uniform six-number subsets of 1–49.

Results · Method · Data · Code

Experiment 02

Hot, cold and random: a genuinely held-out experiment

In each independent trial, rank 49 numbers in 100 training draws, break frequency ties randomly, then freeze three six-number sets and evaluate on 20 fresh draws.

Results · Method · Data · Code

Experiment 03

1-2-3 versus 2-6-9: exact enumeration and one million draws

Enumerate C(10,3)=120 subsets exactly, then sample 1,000,000 uniform 3/10 draws.

Results · Method · Data · Code

Experiment 04

How long can one number stay absent? A million complete waits

Draw one million independent geometric waiting times for a prespecified number with inclusion probability 6/49.

Results · Method · Data · Code

Experiment 05

Consecutive numbers: the exact answer meets a million draws

Count adjacent differences equal to one in each sorted 6/49 draw.

Results · Method · Data · Code

Experiment 06

Two fresh draws, one million times: how many numbers repeat?

Generate one million independent pairs of 6/49 draws.

Results · Method · Data · Code

Experiment 07

Balanced groups, equal tickets: the odd–even experiment

Group one million uniform 6/49 draws by odd count.

Results · Method · Data · Code

Experiment 08

Why any repeat arrives sooner than one chosen repeat

Run 10,000 independent sequences on 10,000 equally likely outcomes, stopping at the first repeated outcome.

Results · Method · Data · Code

Experiment 09

Twenty chances to be fooled: a false-positive experiment

Model 20 independent tests with exactly calibrated 5% false-positive rates as Bernoulli indicators, repeated 100,000 times.

Results · Method · Data · Code

Experiment 10

Closer in proportion, further in count: the law of large numbers

Generate 20,000 independent binomial counts at each sample size.

Results · Method · Data · Code

Experiment 11

An eight-bit die exposes modulo bias

Map one million uniform bytes to six faces with modulo; separately generate one million accepted faces by rejecting bytes 252–255.

Results · Method · Data · Code

Download the complete research materials