House Edge Explained: Casino Games Ranked by Expected Value
Every casino bet has an expected value: what you win or lose on average for each unit you stake, if you could make the same bet forever. The house edge is that number with the sign flipped. It is the single most useful number for comparing games.
Calculating it yourself
Expected value is the sum of every outcome multiplied by its probability. Take a €1 bet on red in European roulette. The wheel has 37 pockets: 18 red, 18 black and one green zero.
EV = (18/37 × +1) + (19/37 × −1) = −1/37 ≈ −2.70%
The same method works for any single-number bet. Straight up on 17 pays 35 to 1:
EV = (1/37 × +35) + (36/37 × −1) = −1/37 ≈ −2.70%
Every standard bet on a European wheel has the same −2.70% expectation. The payouts are set as if the wheel had 36 pockets, and the zero is the casino's margin. An American wheel adds a double zero: 38 pockets, same payouts, so the edge becomes 2/38 ≈ 5.26%.
How the games compare
| Game and bet | House edge | Notes |
|---|---|---|
| Blackjack, basic strategy | ≈ 0.3–1% | Depends heavily on rules; about 0.5% in our simulation |
| Baccarat, banker | 1.06% | After the 5% commission |
| Baccarat, player | 1.24% | |
| Craps, pass line | 1.41% | The "odds" bet placed behind it has no house edge at all |
| Roulette, single zero | 2.70% | Every standard bet |
| Roulette, double zero | 5.26% | Every bet except the five-number bet, which is worse (7.89%) |
| Slot machines | ≈ 2–15% | Set by the operator within legal limits; not visible to the player |
| Baccarat, tie (8 to 1) | ≈ 14.4% | |
| Keno | ≈ 25–29% |
Figures for baccarat, craps, roulette, slots and keno are from the Wizard of Odds house-edge comparison.
What the house edge does not tell you
It is per unit bet, not per session. A 1% edge on blackjack sounds smaller than 2.7% on roulette, but blackjack is dealt much faster. At 80 hands an hour with a €10 bet, 1% costs about €8 an hour. At 35 spins an hour with the same bet, 2.7% costs about €9.50 an hour. The two games cost roughly the same per hour.
It says nothing about the swings. Two bets with the same edge can feel completely different. A red/black bet in roulette and a straight-up bet on one number have the same −2.70% expectation, but the single number wins only once in 37 spins on average. That difference is variance, and it decides how long a bankroll lasts.
It cannot be beaten by bet patterns. Raising and lowering bets according to past results does not change the expectation of any individual bet. We tested the popular systems in roulette betting systems, tested by simulation.
The exception that proves the rule
Blackjack is the only mainstream casino game where the edge can swing to the player. The cards already dealt change the composition of the rest of the shoe. That is what card counting exploits. In every game with independent trials, such as roulette, dice and slots, the house edge is fixed for every bet.
- House edge of casino games compared, Wizard of Odds
- Expected value, Wikipedia
- Roulette, Wikipedia
- Center for Gaming Research, University of Nevada, Las Vegas