House Edge Math: How Casinos Win in the Long Run

House edge is the average percentage of every bet the casino expects to keep over thousands of spins or hands. It’s built into the game’s rules and payouts. It doesn’t mean you lose every time – just that, on average, the math favors the casino.

Think of it like this:
For every $100 wagered, the casino keeps $X and returns $100 – $X to players.
That $X is the house edge.

The Simple Formula

House Edge = 1 – RTP
(RTP = Return to Player)

Or in math:

House Edge (%) = 100% – (Total Payouts ÷ Total Bets) × 100

Example 1: Mini Roulette (Even-Money Bet)

You bet $1 on red.

• Win chance: 6 out of 13 → 6/13 = 46.15%
• Win payout: $1 profit → $2 total back
• Loss chance: 7 out of 13 → 7/13 = 53.85%
• Loss: –$1

Expected Value (EV) per $1 bet:

EV = (Win % × Payout) + (Loss % × Loss)
   = (0.4615 × $1) + (0.5385 × –$1)
   = $0.4615 – $0.5385
   = –$0.077

You lose 7.7 cents per $1 on average.

House Edge = 7.7% ÷ 2 = 3.85%
(Why divide by 2? Because the $1 profit is on top of your stake.)

RTP = 96.15%
House Edge = 100% – 96.15% = 3.85%

Example 2: European Roulette (Single Number)

You bet $1 on number 7.

• Win chance: 1 out of 37 → 1/37 ≈ 2.70%
• Win payout: $35 profit → $36 total back
• Loss chance: 36/37 ≈ 97.30%
• Loss: –$1

Expected Value:

EV = (1/37 × $35) + (36/37 × –$1)
   = $0.9459 – $0.9730
   = –$0.0271

You lose 2.71 cents per $1.

House Edge = 2.71%
RTP = 97.3%

Example 3: Blackjack (Perfect Strategy)

With perfect basic strategy:

• Win chance: ~42.4% → +$1
• Push chance: ~8.5% → $0
• Loss chance: ~49.1% → –$1

EV per $1:

EV = (0.424 × $1) + (0.085 × $0) + (0.491 × –$1)
   = $0.424 – $0.491
   = –$0.005

You lose 0.5 cents per $1.

House Edge = 0.5%
RTP = 99.5%

Example 4: Slots (96% RTP)

A slot says RTP = 96%.

That means:

• For every $100 bet, it pays out $96 on average
• Casino keeps $4

House Edge = 4%

No need to know symbols or paylines – the RTP tells you everything.

Why It Works Over Time

The house edge is small per bet, but over millions of spins, it adds up.

Game	House Edge	$100 Bet → Casino Keeps
Mini Roulette (even)	3.85%	$3.85
European Roulette	2.7%	$2.70
Blackjack	0.5%	$0.50
Slots (96% RTP)	4%	$4.00

You can win short-term – but the math always wins long-term.

Your Takeaway

• Lower house edge = better for you
• RTP + House Edge = 100%
• Check game info – it shows RTP
• Play for fun, not to beat the math

The casino doesn’t cheat – it just uses smart numbers. Now you know how they work.