I. The Definition
The house edge is the casino's long-run expected percentage of each wager. Formally:
House Edge = −E[X] / W
Where E[X] is the expected outcome (positive when player wins on average, negative when player loses), and W is the total amount wagered. The negative sign converts player expected value into casino retention rate.
Example — European roulette straight-up bet on 17:
- Win probability: 1/37 ≈ 0.0270, pays 35 × bet
- Lose probability: 36/37 ≈ 0.9730, pays −1 × bet
- E[X] = (1/37)(35) + (36/37)(−1) = (35−36)/37 = −1/37
- House edge = −(−1/37) / 1 = 1/37 = 2.70%
II. House Edge by Game (Optimal Play)
| Game | House Edge | Notes |
|---|---|---|
| Craps Pass + 100x odds | 0.02% | Effectively break-even; only at El Cortez, Cromwell, online |
| Video Poker (full-pay 9/6 JoB) | 0.46% | Requires optimal strategy + correct pay table |
| Blackjack (perfect basic strategy) | 0.40-0.50% | 6 decks, S17, DAS, 3:2 |
| French Roulette (La Partage) | 1.35% | Even-money bets only; Monte Carlo standard |
| Baccarat Banker | 1.06% | After 5% commission |
| Baccarat Player | 1.24% | |
| Craps Pass Line (no odds) | 1.41% | |
| European Roulette | 2.70% | All bets identical |
| Sic Bo (Big/Small) | 2.78% | |
| American Roulette | 5.26% | The 00 pocket nearly doubles edge |
| Slot Machines (Strip average) | 8.5% | Varies 4-15% by denomination |
| Baccarat Tie (8:1) | 14.36% | Worst common bet on the table |
| Craps Any 7 | 16.67% | |
| Keno | 20-35% | Pace usually slow, masks the damage |
| State Lottery (Powerball) | 50-65% | The worst legal gambling product |
III. House Edge vs Hold Percentage
The two metrics are related but not equivalent:
- House Edge: per-bet expected retention rate. Theoretical, fixed by the game's mathematics.
- Hold Percentage: actual revenue ÷ total cash drop. Reported empirically by casinos to regulators.
Hold is always higher than house edge because players cycle their winnings back into more bets. A blackjack table with 0.5% house edge typically reports 12-16% hold. Why? Average player buys $200 in chips, plays through them with house edge slowly eroding the bankroll, and walks away with $40 left. That's $160 of "cash drop" recovered by the casino — 80% hold percentage at first glance, but the actual house edge across all wagers was only 0.5%.
Casino executives manage hold (the cash-flow metric); players should understand house edge (the cost-per-bet metric).
IV. Why House Edge Doesn't Feel Like 2%
Average Las Vegas Strip visitor: 4-day stay, gambles ~8 hours, average $50 hand bet, ~50 hands/hour at table games. Total exposure: 4 × 8 × 50 × $50 = $80,000 wagered. At blackjack's 0.5% house edge, expected loss = $400. At baccarat's 1.06% = $848. At American roulette's 5.26% = $4,208.
Most players don't experience that exact expected loss because of variance. The standard deviation on $80,000 wagered at 1% house edge with typical $50 bets is about $4,000 — meaning a single trip can swing ±$8,000 from expected value at one standard deviation. Of the casino's customers:
- ~30% leave ahead on a given trip (despite long-run negative expectation)
- ~50% leave slightly behind (within 50% of expected loss)
- ~20% leave catastrophically behind (multiple standard deviations below expected)
The casino doesn't need to win on every trip. It needs to win on average across all trips, all visitors, all years. House edge guarantees this.
V. Variance vs House Edge — The Distinction That Matters
Two games can have the same house edge but radically different volatility:
- Baccarat Banker (1.06%, low variance): most hands resolve ±1 unit. 100 hands rarely deviates more than ±15 units.
- Mega Moolah jackpot slot (~3% edge, extreme variance): most spins lose; rare jackpot of $10M+ inflates RTP nominally but is reached by < 0.001% of players. Effective edge for typical play approaches 12%.
When comparing games, look at both numbers: house edge tells you the average cost; variance tells you how much your experience will deviate from that average. The combination determines your "ruin probability" — the chance of losing your entire stake before any reasonable session length.
VI. Slot Machine Edges — The Hidden Variant
Unlike table games where house edges are mathematically derivable, slot machine edges are determined by the pay table configured in the game's PAR sheet (Probability and Accounting Report). The casino can typically choose among 4-6 different PAR sheets for a given machine model:
| PAR Sheet | Theoretical Edge | Use |
|---|---|---|
| "Tightest" | 10-15% | Low-denomination machines (penny / 2-cent), high foot-traffic areas |
| "Standard" | 6-9% | Most $1 / $5 machines |
| "Loose" | 3-5% | High-denomination ($25+) / VIP rooms / advertising bait |
| "Loosest" (rare) | 1-3% | Marketing promotions, certified loose strips |
The same machine model can have any of these edges depending on PAR sheet selected. Players cannot tell which is in use from the screen — only from cumulative outcomes over thousands of spins. Regulators (UKGC, Nevada NGCB) require periodic disclosure but enforcement is uneven.
VII. The Player's Hourly Cost
The most useful house-edge calculation is expected hourly loss:
Hourly Loss = Bet Size × Hands/Hour × House Edge
| Game | Bet | Hands/hour | Edge | Hourly Loss |
|---|---|---|---|---|
| Blackjack (basic strategy) | $25 | 70 | 0.5% | $8.75 |
| Baccarat Banker | $25 | 60 | 1.06% | $15.90 |
| European Roulette | $25 | 50 | 2.70% | $33.75 |
| American Roulette | $25 | 50 | 5.26% | $65.75 |
| Slot Machine ($1, average) | $3 (3-line) | 600 | 8% | $144 |
| Slot Machine (high-denomination) | $25 | 500 | 4% | $500 |
Switching from American to European roulette saves $32/hour. Switching from slots to basic-strategy blackjack saves $135/hour. These are real, math-certain savings for any regular player.
VIII. Regulatory Disclosure of House Edge
Disclosure requirements vary by jurisdiction:
- UK (UKGC) — every game's RTP / house edge must be publicly disclosed; quarterly reports of actual vs theoretical published
- Malta (MGA) — RTP disclosure required, actuarial monitoring
- Nevada (NGCB) — slots minimum RTP 75%, no requirement to disclose specific PAR sheet
- New Jersey (DGE) — quarterly aggregate hold reports public
- Macau (DICJ) — aggregate revenue reports; per-game edges not publicly disclosed
- Most US state lotteries — explicit RTP rarely disclosed at point of sale
UKGC-licensed online casinos display RTP in every game's help screen. Las Vegas physical casinos almost never do.
IX. Common Misconceptions
- ❌ "Hot streaks change the house edge." Each event is independent. The edge applies in expectation across infinite trials.
- ❌ "Higher payouts mean higher house edge." No. House edge is set by pay-table vs probability ratio, not absolute payout.
- ❌ "5% house edge is fine, that's small." 5% on $80,000 wagered = $4,000 expected loss. Compound across multiple trips and it becomes catastrophic.
- ❌ "VIP rooms have lower house edge." Sometimes (single-zero roulette, better blackjack rules). But also higher bet sizes, so absolute loss rises.
X. FAQ · Sources · Responsibility
How is house edge actually calculated?
House edge vs hold percentage — what's the difference?
Why are slot machine house edges so much higher than table games?
Does house edge change in the short term?
Why is video poker an exception with edges sometimes <0.5%?
What's the highest-house-edge product in legal gambling?
Sources
- Stewart N. Ethier (2010), The Doctrine of Chances: Probabilistic Aspects of Gambling, Springer
- UK Gambling Commission, Industry Statistics — Theoretical vs Actual Returns 2024
- Nevada Gaming Control Board, Annual Gaming Revenue Report 2024
- Michael Shackleford, House Edge Comparison Tables, wizardofodds.com
- Anthony Cabot & Robert Hannum (eds., 2005), Practical Casino Math, Trace Publications