Probability Paradox Lab

3 themes free + 7 premium paradoxes in one purchase. Monty Hall, Birthday, Ellsberg & more — play now!

"With 23 people in a class, what's the chance two share a birthday?"

The answer exceeds 50%. Were you surprised?

Probability Paradox Lab is an interactive app that lets you experience mathematical paradoxes through simulation — results that feel wrong, yet are mathematically proven.

[ HOW IT WORKS ]

1. Make your intuitive guess
2. Run the simulation and see the real result
3. Read the math explanation and understand why

Be surprised by the answer. Be surprised again by the explanation.

[ FREE THEMES ]

Birthday Problem (Free) With just 23 people, the probability of a shared birthday exceeds 50%. Why?

Monty Hall Problem (Free) After the host opens a losing door, switching wins 2/3 of the time. Mathematically proven — yet deeply counterintuitive.

Two Envelopes Problem (Free) A seemingly valid argument says you should always switch envelopes. Where's the flaw?

[ PREMIUM THEMES ]

One-time purchase unlocks 7 more paradoxes. No subscriptions, no ads for premium users.

Ellsberg Paradox Why do people prefer known odds over unknown ones — even when the math says they're equal?

Boy or Girl Paradox "One child is a boy." How does that single fact change the probability?

Nontransitive Dice (Efron-style) A beats B, B beats C, C beats A. No die is the strongest.

Parrondo's Paradox Two losing games, played in alternation, somehow become a winning strategy.

Simpson's Paradox A treatment wins in every subgroup — yet loses overall. How?

St. Petersburg Paradox Expected value is infinite, yet you'd pay little to play. Why?

Friendship Paradox Your friends have more friends than you — the network bias that makes it true.

[ PERFECT FOR ]

• Math & statistics enthusiasts
• Curious minds who love "why?"
• Brain teaser & trivia fans
• Students and lifelong learners