Priors
All puzzles
50 probability and expected-value puzzles. Guess first, then solve, then watch the simulation.
Conditional probability
- A six is showing · Board games
- At least one boy · Family
- The flagged transaction · Fraud detection
- The host knows · Game show
- The two-headed coin · Magic shop
- The rich get richer · Lucky draw
- Which ace did they see? · Teen patti
Counting and complements
- The Chevalier's bet · Dice
- Best of three · Sports
- Birthdays in the locker room · Sports
- Exactly one pair · Poker
- Never going down · Dice
- The unlucky second seed · Badminton
- No couple side by side · Wedding dinner
- Nobody draws themselves · Office party
- Ahead all night · Election counting
Expectation
- Counting streaks · Coin flips
- The best of the dice · Dice
- All-time highs · Stock market
- Collect every team card · Collectibles
- Empty subway cars · Subway
- Heads in a row · Coin flips
- Every face on a loaded die · Dice
- Nobody sits next to a stranger · College cafeteria
- Socks in the dark · Home
- Until the total passes · Random numbers
- Waiting for an ace · Cards
- Waiting for the shuttle bus · Commuting
Bets and decisions
- To guess or not to guess · Exam strategy
- A call option on dice · Trading desk
- Chasing the flush · Poker
- The one-claim warranty · Electronics store
- A portfolio of moonshots · Startup investing
- The St. Petersburg casino · Casino
- What is a peek worth? · Game show
- Pays if it ever touches · Trading desk
- Too much of a good bet · Investing
Geometric probability
- Meeting at the station · Commuting
- Across the running track · Athletics
- Break the stick · Geometry
- Does it hold the center? · Geometry
- How far from the bullseye · Darts
- The needle on the floorboards · Geometry
- The smooth stretch outside your house · City roads
- Two riders, one square · Delivery
Games and stopping
- Keep or reroll · Dice game
- Will you land on it? · Board games
- A small edge, a big gap · Betting
- Lost on the subway · Subway
- Hire on the spot · Startup hiring