Themes · wave 1
Probability Paradoxes
Chance is the part of maths where intuition fails most often, and most confidently. Every gem in this theme follows the same recipe: make a guess, play the game a thousand times, then find out why the guess was wrong.
Gems
The Monty Hall Problem
Three doors, one car, two goats. The host opens a door with a goat. Should you switch?
The Birthday Paradox
How many people do you need in a room before two of them probably share a birthday? Far fewer than you think.
The Two Envelopes Paradox
One envelope holds twice as much as the other. A simple argument says you should always swap. Why is it wrong?
Parrondo's Paradox
Two coin games that both lose money in the long run. Mix them up, and you start winning. How?
The Elevator Paradox
You work near the top of a tall building and want to go down. Why is the first elevator to arrive nearly always going up?
Simpson's Paradox
One player is better at close shots and at long shots, yet has the worse score overall. How can both be true?
Bertrand's Paradox
Draw a random chord in a circle. Is it longer than the side of the inscribed triangle? Three honest methods give three different answers.
A Die from a Coin
A coin has two sides and a die has six. Can a fair coin roll a fair die, or give a chance of exactly one in three?
Braess's Paradox
A town opens a new road, and every single driver gets to work later. How can more roads mean slower traffic?