The House Always Wins: The House Edge

How casinos and betting operators build a mathematical edge into every game so they profit over many bets, and why expected value is negative for players.

Gambling operators build in a house edge.

Expected value

The expected value of a bet is the average win or loss per bet over many plays. For players, it’s negative.

Example

In European roulette, there are 37 pockets (1-36 plus 0). A bet on one number pays 35 to 1, but the true odds are 36 to 1, giving the house an edge of about 2.7%.

Law of large numbers

Individual players may win, but over millions of bets the casino reliably earns its edge.

Betting margins

Bookmakers set odds so implied probabilities add up to more than 100%; the extra is their margin.

Economics

Gambling is a business selling entertainment and hope, priced through the house edge.

The lucky night

A player wins big one night, but across all players that month, the casino earns close to its expected edge.

Thinking skill can beat pure chance games over time

The house edge wins in the long run.

Key takeaways

The house edge makes expected value negative.
European roulette's edge is about 2.7%.
The law of large numbers guarantees profits.
Bookmakers build margins into odds.