Interactive Paradoxes
An interactive sandbox for statistical paradoxes and probability illusions. Each exhibit lets you change the numbers and see for yourself why intuition and math disagree.
Belief Revision & Coincidence
Exploring how human intuition fails to grasp the implications of massive scales and vast opportunities.
Clustering Illusions
How genuine randomness produces clumps, gaps, and streaks, and why we so often read them as meaningful or as “not random.”
The Clustering Illusion
Random events don’t spread themselves out: genuine randomness produces clumps and gaps, while an unusually even pattern can contain more structure than a random one.
Human-made Randomness
When people try to imitate a fair coin, they typically switch outcomes more often than chance would, and avoid the long runs that real randomness naturally produces.
Random Streaks
In 50 fair coin flips, a streak of 5 or more in a row happens about 82% of the time, and 6 or more happens more often than not.
This Couldn't Just Be Coincidence!
A striking local pattern can come from pure chance or from a genuinely non-random process, and can look the same either way at first glance.
The Egocentric Blind Spot
Paradoxes that trick us by making us focus on our personal perspective rather than the entire network.
Hidden Structures in Chaos
Investigating statistical laws that govern seemingly random or chaotic datasets.
Benford's Law (The First-Digit Anomaly)
In many real-world datasets, numbers are much more likely to begin with smaller digits than larger ones.
The Inspection Paradox (Bus Stop Bias)
When you arrive at a random time, you’re more likely to encounter a long interval than a short one.
Simpson's Paradox
A trend appears in several separate groups but reverses or disappears when the groups are combined.
The Prosecutor's Fallacy (Base-Rate Neglect)
People focus on how strong or unusual one piece of evidence seems while ignoring how common the underlying situation is to begin with.
New Information & Changing Odds
How new information from a knowledgeable source should change the odds you assign to what you already picked.
Psychological Effects
Not mathematical paradoxes, but cognitive and memory biases that distort how we judge track records and evidence.