The house edge
Spin a roulette wheel a thousand times, then watch a thousand players do it. The house never loses.
- Spins
- 0
- Wagered
- $0
- You are
- $0
- Expected
- $0
- Your return per $1
- –
- House edge
- −2.70%
A thousand players
One person can get lucky. Simulate 1,000 players each betting $10 a spin for 1,000 spins and see who the wheel pays.
What’s going on
A European wheel has 37 pockets: 18 red, 18 black and one green 0. A $1 bet on red wins $1 with probability 18/37 and loses $1 with probability 19/37, so its expected value is 18/37 − 19/37 = −1/37 ≈ −2.70% of every dollar bet. The American wheel adds a 00, which makes it −2/38 ≈ −5.26%.
A single number pays 35 to 1 and wins 1 time in 37: 35 × 1/37 − 36/37 = −1/37. Same edge, far more variance. That is why more of the crowd is still ahead after betting on 17 than after betting on red, while the average loss is the same.
The law of large numbers is the casino’s business model: any one player’s results swing wildly, but the average over millions of spins lands on the edge, and the casino is the only player who makes millions of spins.
For learning, not gambling advice.