when intuition lies
Paradoxes.
Cases where the right probability answer feels clearly wrong.
6 live pieces
· 18
more on the way
Monty Hall
Switch or stay? Simulate the game and watch win rates diverge.
Base rate neglect
A 99% accurate test for a rare disease — what does a positive really mean?
Simpson's paradox
A trend holds in every subgroup but reverses when pooled. Adjust case mixes to see it flip.
Gambler's fallacy
After five heads, tails must be due — right? Running proportions expose the error.
St. Petersburg paradox
A game with infinite expected value — yet no one would pay much to play. Expected value breaks down.
Two envelopes paradox
A compelling argument says switching always wins. Simulation shows both strategies tie at 50%.
Boy or girl paradox
soon 1/2 or 1/3? The answer depends on how you sampled the information.
Bertrand's box paradox
soon Gold and silver coins in three boxes. A crisper cousin of Monty Hall.
Sleeping Beauty
soon Thirder or halfer? Simulate many awakenings and count each framing.
Bertrand paradox
soon Three natural samplers of a random chord give three different probabilities.
Borel's paradox
soon Conditioning on a measure-zero event depends on how you parameterize.
Inspection paradox
soon Buses arrive every 10 minutes but you wait 7. Why size-biased sampling lies.
Friendship paradox
soon Your friends have more friends than you do. A graph-sampling artefact.
Berkson's paradox
soon Conditioning on admission makes independent traits look correlated.
Parrondo's paradox
soon Two losing games combine into a winning strategy. Alternation breaks the bias.
Non-transitive dice
soon A beats B, B beats C, C beats A. Probability doesn’t respect ordering.
Penney's game
soon Pick a coin-flip pattern; your opponent picks one that beats it. Non-transitive.
Ellsberg paradox
soon Two urns, one known, one ambiguous. Ambiguity aversion breaks expected utility.
Allais paradox
soon The certainty effect distorts rational choice between two lottery pairs.
Lindley's paradox
soon Frequentist rejects; Bayesian favors the null. Same data, opposite conclusions.
Newcomb's problem
soon One box or two? Causal and evidential decision theory disagree.
Will Rogers phenomenon
soon Moving a patient from one group to the other raises the average of both.
Accuracy paradox
soon With 1% positives, a do-nothing classifier is 99% accurate. Why accuracy misleads.
Doomsday argument
soon Self-sampling priors push the expected end-date alarmingly close.