What is House Edge?
The house edge is the mathematical advantage that the casino holds over players in any given game. It represents the average percentage of each bet that the casino expects to keep over the long run. This built-in advantage ensures casinos remain profitable while still allowing players to win in the short term.
The Casino Business Model
Casinos don't need to cheat or rig games. The house edge guarantees profitability through the law of large numbers. While individual players may win big, the casino's edge ensures they profit from the collective action of all players over time.
House Edge vs Player Return
House Edge
The percentage the casino expects to keep from every bet placed.
Example: 5% house edge
Casino keeps $5 per $100 bet
Player Return (RTP)
The percentage returned to players over time from every bet placed.
Example: 95% RTP
Players get $95 per $100 bet
Critical Understanding
House Edge + RTP = 100%
These are two ways of expressing the same concept. A game with a 2% house edge has a 98% RTP. The house edge tells you what the casino keeps; RTP tells you what players collectively receive back.
Mathematical Foundation of House Edge
The house edge is rooted in probability theory and the concept of expected value. Every casino game is designed with specific probabilities that slightly favor the house.
The Probability Formula
House Edge = Σ(Probability × House Gain)
For all possible outcomes
Example: European Roulette
Let's calculate the house edge for a single number bet in European Roulette:
Expected Value Calculation:
(1/37 × 35) - (36/37 × 1) = -0.027
House Edge: 2.7%
The Law of Large Numbers
The law of large numbers ensures that as more bets are placed, the actual results converge toward the theoretical house edge:
| Number of Bets | Expected Deviation | Accuracy Range |
|---|---|---|
| 100 | ±10% | -7.3% to +12.7% |
| 1,000 | ±3.2% | -0.5% to +5.9% |
| 10,000 | ±1% | 1.7% to 3.7% |
| 100,000 | ±0.32% | 2.38% to 3.02% |
| 1,000,000 | ±0.1% | 2.6% to 2.8% |
Expected Value Calculations
Expected value (EV) is the average amount you can expect to win or lose per bet if you were to place the same bet many times. Understanding EV is crucial for evaluating any gambling proposition.
Expected Value Formula
EV = Σ(Probability of Outcome × Value of Outcome)
Negative EV = House advantage
Positive EV = Player advantage (rare)
Real-World EV Examples
Coin Flip Bet (Fair Game)
Setup:
- • Bet: $10
- • Win: Get $20 (profit $10)
- • Lose: Lose $10
- • Probability: 50/50
Calculation:
EV = (0.5 × $10) + (0.5 × -$10)
EV = $5 - $5 = $0
Result: No house edge
Blackjack (Basic Strategy)
Setup:
- • Bet: $100
- • Win rate: 42.4%
- • Loss rate: 49.1%
- • Push rate: 8.5%
Calculation:
EV = (0.424 × $100) + (0.491 × -$100) + (0.085 × $0)
EV = $42.40 - $49.10 = -$0.50
House Edge: 0.5%
Slot Machine (96% RTP)
Setup:
- • Bet: $1 per spin
- • RTP: 96%
- • House Edge: 4%
- • 1000 spins
Expected Loss:
Total Wagered = $1 × 1000 = $1000
Expected Return = $1000 × 0.96 = $960
Expected Loss = -$40
Loss per spin: -$0.04
The Gambler's Fallacy
Expected value doesn't change based on previous results. Each bet is independent. After losing 10 blackjack hands in a row, your next hand still has the same 0.5% house edge. The casino's advantage never disappears.
Casino Games Ranked by House Edge
Not all casino games are created equal. The house edge varies dramatically between games and even between different bets within the same game.
Complete Game Comparison
| Game/Bet | House Edge | RTP | Notes |
|---|---|---|---|
| Best Odds (Under 1%) | |||
| Blackjack (Basic Strategy) | 0.28-0.5% | 99.5-99.72% | Requires perfect play |
| Craps (Pass/Don't Pass) | 0.6% | 99.4% | With odds bets |
| Baccarat (Banker) | 1.06% | 98.94% | 5% commission on wins |
| Moderate Odds (1-3%) | |||
| Baccarat (Player) | 1.24% | 98.76% | No commission |
| Craps (Field Bet) | 2.78% | 97.22% | Single roll bet |
| European Roulette | 2.7% | 97.3% | Single zero wheel |
| Three Card Poker (Pair Plus) | 2.32% | 97.68% | Side bet only |
| Poor Odds (3-6%) | |||
| Three Card Poker (Ante) | 3.37% | 96.63% | With optimal play |
| Let It Ride | 3.51% | 96.49% | Popular poker variant |
| Slot Machines (Vegas Strip) | 4-8% | 92-96% | Varies by casino |
| American Roulette | 5.26% | 94.74% | Double zero wheel |
| Terrible Odds (Over 6%) | |||
| Caribbean Stud | 5.22% | 94.78% | Progressive side bet worse |
| Roulette (Five Number) | 7.89% | 92.11% | Worst roulette bet |
| Craps (Any 7) | 16.67% | 83.33% | Single roll sucker bet |
| Wheel of Fortune | 11-24% | 76-89% | Depends on bet |
| Keno | 25-40% | 60-75% | Lottery-style game |
Special Situations
Video Poker (Full Pay)
- • Jacks or Better (9/6): 0.46% edge
- • Deuces Wild: -0.76% (player advantage!)
- • Double Bonus (10/7): -0.17% (player advantage!)
*With perfect play
Blackjack Variations
- • Single deck: 0.17% edge
- • 6 decks: 0.46% edge
- • 6:5 blackjack: 1.39% edge (avoid!)
*With basic strategy
Long-Term Expectations
Understanding how the house edge affects your bankroll over time is crucial for responsible gambling. Let's examine what happens to $1,000 over different time periods and games.
Expected Loss Calculator
Expected Loss = (Total Wagered) × (House Edge)
Total Wagered = (Bet Size) × (Bets Per Hour) × (Hours Played)
Hourly Loss Expectations
| Game | Bets/Hour | $25 Bet Loss/Hour | 8-Hour Loss |
|---|---|---|---|
| Blackjack (0.5%) | 80 | $10 | $80 |
| Baccarat (1.06%) | 100 | $26.50 | $212 |
| Craps (0.6%) | 50 | $7.50 | $60 |
| Roulette (2.7%) | 40 | $27 | $216 |
| Slots (5%) | 600 | $750 | $6,000 |
| Video Poker (0.5%) | 400 | $50 | $400 |
The Compounding Effect
Starting with $10,000 and playing slots at $5 per spin (600 spins/hour) with 5% house edge:
After 10 hours
-$1,500
$8,500 remaining
After 50 hours
-$7,500
$2,500 remaining
After 67 hours
-$10,000
Bankroll depleted
Variance and Short-Term Results
While the house edge determines long-term results, short-term variance can produce wildly different outcomes:
Strategies to Reduce the House Edge
While you can't eliminate the house edge, you can minimize it through smart choices and optimal play.
1. Choose the Right Games
- ✓Play blackjack with good rules (3:2 blackjack, surrender allowed)
- ✓Choose European roulette over American (2.7% vs 5.26%)
- ✓Look for full-pay video poker machines
- ✗Avoid side bets and progressive jackpots (unless life-changing)
2. Learn Optimal Strategy
- →Blackjack: Basic strategy reduces edge from 2% to 0.5%
- →Video Poker: Perfect play can achieve 99.5%+ RTP
- →Craps: Stick to pass/don't pass with odds
- →Baccarat: Always bet banker despite commission
3. Take Advantage of Comps
- • Cashback programs can reduce effective house edge by 0.2-0.5%
- • Free play offers provide value without additional risk
- • Comp points for meals and rooms offset gambling costs
- • Loss rebates soften the blow of bad sessions
Example: 0.3% cashback on slots with 3% house edge = 2.7% effective edge
4. Bankroll Management
- • Set loss limits and stick to them
- • Never chase losses with bigger bets
- • Play at cobras appropriate for your bankroll
- • Take breaks to avoid fatigue-induced micobras
5. Avoid These House Edge Traps
- ⚠6:5 Blackjack: Increases house edge by 1.39%
- ⚠Side Bets: Usually 3-7% house edge or worse
- ⚠Tie Bet in Baccarat: 14.4% house edge!
- ⚠Insurance in Blackjack: 7.4% house edge
Frequently Asked Questions
Can the house edge be overcome?
In most games, no. The house edge is mathematically built into the game rules. However, advantage play techniques like card counting in blackjack or finding positive EV video poker machines can create a player edge. These opportunities are rare and casinos actively work to eliminate them.
Why do casinos offer games with low house edges?
Low house edge games attract knowledgeable players and create an atmosphere of fairness. These games also generate consistent profits through volume. Additionally, most players don't play optimally, so the effective house edge is higher than the theoretical minimum.
Does betting more reduce the house edge?
No, the house edge percentage remains the same regardless of bet size. However, some games offer better odds for higher denominations (like slots) or maximum bets (like video poker with the royal flush bonus). The mathematical edge doesn't change, but the game rules might be more favorable.
How long does it take for the house edge to manifest?
The house edge becomes apparent over thousands of bets. In a single session, variance dominates and anything can happen. Generally, after 10,000 bets, results should be within 1-2% of the expected house edge. After 100,000 bets, you'll be very close to the theoretical edge.
Which has better odds: table games or slot machines?
Table games generally offer much better odds. Blackjack (0.5%), baccarat (1.06%), and craps (0.6%) all beat typical slot machines (2-10% house edge). However, table games require knowledge and decision-making, while slots are purely chance-based and easier to play.
Key Takeaways
- ✓The house edge ensures casinos profit over time through mathematical advantage
- ✓Games vary widely in house edge, from 0.5% (blackjack) to 40% (keno)
- ✓Optimal strategy can significantly reduce but not eliminate the house edge
- ✓Short-term variance masks the edge, but long-term results converge to expectations
- ✓Understanding house edge is essential for responsible gambling
- ✓The best defense is game selection, optimal play, and strict bankroll management
See House Edge in Real-Time
Experience how house edge affects your bankroll with our advanced casino simulator. Run thousands of bets and watch the mathematical edge emerge.