Lab 10 / Uncertainty
Why fair sequences form streaks
How unusual is the longest run in one fair sequence?
Generate binary sequences, count their runs, and compare independent trials with a mechanism that alternates too often. Change one control at a time, then open the values under the chart before interpreting the picture.
View the values behind this chart
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SEEDInterpret the result
The paired guide explains the mechanism, assumptions, and cases where this display should not be generalized.
What this display answers
Independent fair outcomes do not need to alternate. Runs and clusters are valid outputs, and longer sequences create more places for a memorable streak to occur.
The repeated histogram puts the longest run from one displayed sequence into context. Raising the switch chance above 50% creates too many alternations and shortens typical longest runs even though heads and tails can remain balanced.
What to notice
- At a 50% switch chance, read the displayed sequence and count its runs before comparing it with the repeated summary.
- Increase sequence length. Typical longest runs grow because the sequence offers more opportunities for one.
- Set switch chance to 80%. The mean run count rises sharply and long same-symbol streaks become less common.
The model behind it
The first symbol is equally likely to be H or T. Every later symbol switches from the previous one with the selected probability.
A 50% switch chance is equivalent to independent fair Bernoulli trials. Other settings deliberately introduce serial dependence and are included for comparison, not as models of a physical coin.
Where the result stops
One ordinary run count does not prove randomness, and one long streak does not disprove it.
The browser generator is deterministic from its seed and is not intended for security, gambling, or prediction.