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Understanding the House Edge

by Rajat Chatterjee ·

mathematicshouse-edgefundamentalsprobability

The Number That Never Sleeps

The house edge is the casino's average profit, expressed as a percentage of your total wagered amount. It's not the amount you lose per visit—it's a mathematical certainty across millions of bets.

Understanding the house edge doesn't eliminate it. It helps you choose better bets and set realistic expectations.

Calculating the House Edge on a Straight-Up Bet

A straight-up bet (single number) on a European roulette wheel pays 35 to 1. But the true odds of winning are 1 in 37 (37 pockets total).

True odds payout: 36 to 1 (pay 36, keep stake) Casino payout: 35 to 1

The house keeps one unit of every 37 wagered:

House Edge = (36 - 35) / 37 = 1/37 = 2.70%

Correct calculation for American: you get paid 35:1 but there are 38 pockets, so expected value per dollar = (35 × 1/38) + (-1 × 37/38) = 35/38 - 37/38 = -2/38 = -5.26%

Every Bet Has the Same Edge on a Given Wheel

On a European wheel, every bet has the same 2.70% house edge except for certain French rules. The bet type (inside vs outside, odd/even vs corner) doesn't change the edge.

This means the "best" bets on a straight roulette wheel aren't about the type of bet—they're about variance management.

What the House Edge Means Over Time

With a 2.70% house edge, if you bet $100/spin for 500 spins:

  • Total wagered: $50,000
  • Expected loss: 2.70% × $50,000 = $1,350

The house edge is relentless. It grinds.

Variance vs Edge: Two Different Things

The house edge tells you the long-run expectation. Variance tells you how wild the ride can be.

Betting on individual numbers (straight-up) is high variance—big wins, big losses, but the same edge as outside bets. Betting on even/odd is low variance—many small wins/losses, same edge.

Your choice of bet type is a choice about variance, not edge.

Games You Should Avoid vs Accept

Roulette with La Partage: 1.35% house edge—among the lowest in the casino. European roulette: 2.70%—reasonable. American roulette: 5.26%—nearly twice European. Avoid. The Five-Number Bet (American only: 0, 00, 1, 2, 3): 7.89%—the worst bet on the wheel.

The Honest Takeaway

No strategy eliminates the house edge. It's math. What you control: which variant you play, how long you play, how much you bet, and how you manage your bankroll. The rest is probability.

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