The House Always Wins
Statistics & Probability
Investigate common casino games.
Introduction
Casino games are built so that the expected value of every bet favours the house by a fixed, known margin — the house edge. This exploration works out that edge for real bets, tests how bet choice and betting systems change the player's experience without changing the underlying expected value, and simulates what actually happens to a bankroll over an evening of play.
Guiding Questions
- Pick a casino game — roulette is simplest. Calculate the expected value of each common bet.
- All bets lose on average. Which lose slowest, and does bet choice matter in the long run?
- Simulate an evening of play: how do bankrolls evolve? How likely is walking away ahead?
- Betting systems like Martingale claim to beat the house. Model one and show what actually happens.