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What Is House Edge?
House Edge, also known as the casino advantage, is the percentage of each bet that the casino is expected to keep over the long run as a mathematical profit. Simply put, it represents the casino’s average expected earnings from every wager placed. This figure is a key component in how casinos design game rules to ensure profitability. The house edge is the result of the game’s rules and payout structure. While players may win in the short term, the mathematical design guarantees that the casino maintains steady profits over time.
Mathematical Definition of House Edge:
Mathematically, the formula for house edge is:
- House Edge = (1 − Player Expected Value) × 100%
or, expressed directly as:
- House Edge = (Casino’s Average Winnings / Total Amount Wagered by Players) × 100%
Characteristics of House Edge:
- Long-Term Nature: The house edge reflects the casino’s average profit over the long run. It does not guarantee profit in a single round, but over a large number of games, the house edge will consistently take effect.
- Percentage Expression: The house edge is usually expressed as a percentage. For example, if a game has a house edge of 5%, it means the casino earns an average of $5 for every $100 wagered by players.
- Design Principle: Casinos adjust payout odds or game rules to control the house edge, ensuring both attractiveness to players and profitability. For example, in baccarat, a 5% commission is charged on Banker wins to balance out the higher probability of winning on Banker bets.
House Edge Calculation Example (using Baccarat):
- Banker
- Odds： 1:0.95
- Probability of Banker Win： 45.86%（0.458597）
- Probability of Banker Loss： 54.14%（0.541403）
- Calculation Formula：
- Expected Value = （0.458597 × 0.95）−（0.541403 × 1）
- Expected Value = 0.435667 − 0.541403 = −0.010579
On average, the player loses approximately 0.010579 units per 1 unit bet.
- House Edge：
- House Edge = −Expected Value × 100%
- House Edge = 0.010579 × 100% = 1.06%
The house edge for the Banker bet is 1.06%.
- Player
- Odds： 1:1
- Probability of Player Win： 44.62%（0.446247）
- Probability of Player Loss： 55.38%（0.553753）
- Calculation Formula：
- Expected Value = (0.446247 × 1) − (0.553753 × 1)
- Expected Value = 0.446247 − 0.553753 = −0.107506
On average, the player loses approximately 0.107506 units per 1 unit bet.
- House Edge：
- House Edge = −Expected Value × 100%
- House Edge = 0.107506 × 100% = 1.24%
The house edge for the Player bet is 1.24%.
- Tie
- Odds： 1:8
- Probability of Tie： 9.52%（0.095156）
- Probability of No Tie： 90.48%（0.904844）
- Calculation Formula：
- Expected Value = (0.095156 × 8) − (0.904844 × 1)
- Expected Value = 0.761248 − 0.904844 = −0.143596
On average, the player loses approximately 0.143596 units per 1 unit bet.
- House Edge：
- House Edge = −Expected Value × 100%
- House Edge = 0.143596 × 100% = 14.36%
The house edge for the Tie bet is 14.36%.
Relationship Between House Edge and Player Strategy:
- Choose Games with a Low House Edge:
In baccarat, Banker (1.06%) has the lowest house edge and is the most rational option for long-term betting. - Avoid Options with a High House Edge:
Tie (14.36%) may offer high payouts, but it results in the greatest long-term losses and is not recommended. Use Expected Value as a Guide: The house edge is directly reflected in the expected value—the smaller the negative EV, the less the player loses.
Conclusion:
- House edge is the mathematical foundation that ensures casino profitability—player losses are inevitable over the long run.
- Choosing betting options with a lower house edge (such as Banker) helps minimize losses as much as possible.
- Understanding house edge allows players to develop more rational betting strategies and avoid unnecessary high-risk wagers.
Further Reading: