The arithmetic that fixes every roulette outcome before the ball is spun.

Editorial illustration for the lesson on house edge, the actual maths, in the Mayfair Casino School.
Editorial illustration for the lesson on house edge, the actual maths, in the Mayfair Casino School.

House edge, the actual maths

Annabel Cavendish
Annabel Cavendish
Editor · 14 May 2026

Where the Edge Comes From

Start with the hardware. A European single-zero wheel has 37 pockets numbered 0 through 36. A straight-up bet on one number pays 35 to 1. If the game were fair, it would pay 36 to 1, because there are 36 other possible outcomes for every number you choose. The casino pays 35, not 36: the difference is exactly 1/37 of every pound wagered on that bet. Expressed as a percentage: 1 divided by 37 equals 0.02703, or 2.703%. The decimal never terminates. In practice you see it rounded to 2.70%.

That fraction, 1/37, is embedded identically into every payout on the European table. A split covers two numbers at 17 to 1; fair odds would be 35/2 = 17.5. The shortfall is 0.5/37, which reduces to 1/37 per unit staked. A corner covers four numbers at 8 to 1; fair odds would be 33/4 = 8.25. Shortfall per unit: 1/37. Even-money bets cover 18 numbers at 1 to 1; fair odds would be 19/18 = 1.056. The shortfall comes through zero: when zero lands, the casino takes the even-money bet. Zero lands 1 time in 37, costing you 1/37 of every even-money wager. All roads lead to the same fraction. This is the algebraic identity the spoken lesson references: it's not a coincidence built into the payouts, it's a structural consequence of having one more pocket than the payout schedule acknowledges.

American Double-Zero and the Basket Exception

An American wheel adds a 00 pocket to the 0 through 36 arrangement, giving 38 pockets total. A straight-up bet still pays 35 to 1. Fair payout on 1 in 38 odds would be 37 to 1. The shortfall is 2/38 = 5.263%. Every standard American bet carries this edge, almost twice the European figure for the same physical game with the same dealer and the same playing experience. The sole reason for the difference is the extra pocket.

The five-number basket bet on the American wheel covers 0, 00, 1, 2, and 3. It pays 6 to 1. The fair payout for covering 5 of 38 pockets would be 33/5 = 6.6 to 1. The casino rounds to 6, not 6.6, because 33 isn't divisible by 5. That rounding creates an edge of 7.895%, per Wizard of Odds. It's the only standard roulette bet with a house edge higher than the wheel's own headline figure. Every other American bet is 5.26%. The basket is 7.89%. There's no reason to place it.

Empire Casino at Leicester Square runs American double-zero roulette exclusively, per the venue's published table information. A player sitting at the Empire pays 5.26% on every bet regardless of whether they've chosen a straight-up, a dozen, or red. The postcode is Zone 1 Central London. The mathematics is Nevada.

La Partage and the Annual Cost of Getting It Wrong

La Partage is a French rule that changes what happens when zero lands on even-money bets. Instead of losing your entire stake, you recover half of it. The mathematics is straightforward: zero lands 1 time in 37 on average. Without La Partage, you lose 1 unit when zero lands, so the expected loss from zero on an even-money bet is 1/37 of your stake. With La Partage, you lose only half a unit when zero lands, so the expected loss from zero is 0.5/37 = 1.351%. Exactly half the standard European edge.

The practical annual cost of this difference is not abstract. At £100 per spin, 50 spins per hour, playing even-money bets: £5,000 wagered per hour. At 2.70%, expected cost per hour is £135. At 1.35%, expected cost per hour is £67.50. The difference is £67.50 per hour. Over 100 hours of annual play, that's £6,750 per year, simply from sitting at a European table rather than a French one for your even-money bets. The venues are different, the table minimum and maximum may differ, but the calculation is the same: £100 x 50 x 100 x (2.70% - 1.35%) = £6,750.

Aspers Westfield Stratford confirms La Partage on its European tables, making it the best standard edge available at a UK land-based casino floor on even-money bets. The Hippodrome in Leicester Square and Les Ambassadeurs in Hamilton Place run European tables; players should confirm La Partage availability directly with each venue, as it isn't universally offered even on single-zero tables. Evolution's French Roulette Gold and Auto Roulette La Partage apply the rule online, as confirmed by Evolution's product catalogue.

Why the House Edge Is a Per-Spin Tax, Not a Per-Session Budget

A common misreading of the house edge treats it as a percentage of starting bankroll. It isn't. It's a percentage of total amount wagered. If you bring £1,000 and make 100 bets of £10, you've wagered £1,000 total. Expected loss: £27. If you bring £1,000 and make 100 bets of £100 on an up-and-pull system where you sometimes win and reinvest, you may have wagered £7,000 total before the session ends. Expected loss: £189, even though you started with only £1,000. The edge accumulates on action, not on bankroll. Progression systems that inflate bet sizes after wins increase expected loss in direct proportion to the additional action they generate.

The Zero-Free Interlude and What It Proves

There's a brief historical moment that illustrates the edge calculation with unusual clarity. For roughly a year in late 1967 and into 1968, several London casino rooms removed the zero from their roulette wheels following Scotland Yard's warning of 30 December 1967 that a zero-bearing wheel might be prosecuted under the Betting and Gaming Act 1960. A wheel with 36 pockets and no zero has no house edge on even-money bets: there's no 37th pocket for the casino to withhold. The even-money bet becomes a genuine 50/50 proposition. The Gaming Act 1968 resolved the situation by explicitly authorising the modest house edge as a licensing term, restoring the zero and with it the 2.703% fraction that governs every London table today. The historical episode confirms the edge's source precisely: remove the zero and the even-money edge disappears. The zero is the entire mechanism.

Key numbers

Wheel / RulePocketsHouse edgeAnnual cost (£100/spin, 50 spins/hr, 100 hrs, even-money)
European single-zero372.703%£13,515
European + La Partage371.351%£6,755
American double-zero385.263%£26,315
American basket bet387.895%N/A (inside bet; different variance)
Zero-free (London 1967-68)360%£0 (historical only)
Annabel
0:000:00

Today we're doing the maths.

I'm Annabel, and I want to talk to you about the house edge, which is a phrase that gets thrown around constantly at roulette tables and understood, at a fundamental level, by almost nobody sitting at them.

By the end of this lesson you will understand it precisely, and more usefully, you'll understand what it costs you in pounds per hour at various bet sizes, which is the number that actually matters.

Let's start with European roulette.

There are thirty-seven numbers on the wheel, zero through thirty-six.

When you bet on a single number, it pays thirty-five to one.

The fair payout would be thirty-six to one, because there are thirty-six other outcomes, and the casino keeps one pocket's worth of your money.

That fraction is one thirty-seventh of everything wagered.

In percentage terms, that is two point seven zero three percent.

The decimal never terminates.

The casino rounds payouts down, always, never up, and that rounding is the source of the entire house advantage.

Here is the elegant and slightly maddening fact about European roulette: every single bet on the table, all thirty-five of them, has exactly the same house edge of two point seven percent.

Straight-ups, splits, streets, corners, columns, dozens, red and black, odd and even, high and low.

Every single one.

This is not a coincidence but an algebraic identity baked into the payout structure.

There is exactly one exception on any standard roulette table in the world, and it's on the American wheel.

The fair payout would be six point two to one, because five numbers in thirty-eight pockets gives you a slightly different ratio.

Six doesn't divide neatly into thirty-six plus two, so the casino rounds it down to six, creating a house edge of seven point eight nine five percent on that specific bet.

Every other American wheel bet costs you five point two six percent.

The basket bet costs you seven point eight nine.

Simply don't play it.

Now.

Standard deviation.

This is where most conversations about roulette bet types get it wrong.

The house edge is identical regardless of bet type on a European wheel.

On red and black, it's approximately zero point nine nine nine times your stake.

Same expected loss.

About six times more volatility.

If your goal is session longevity on a fixed budget, outside bets give you that.

If your goal is a meaningful win against a meaningful stake, inside bets are the mechanism.

The house doesn't give you better odds for choosing one over the other.

The edge is the same.

The ride is not.

Let's make this concrete with some hourly numbers, because I think round numbers are more useful than percentages when you're planning an evening.

At five hundred pounds flat, it's four hundred and five pounds an hour.

At five thousand pounds flat, it's four thousand and fifty-four pounds an hour.

That last number is the one worth sitting with.

A four-hour session at five thousand pounds flat on a European wheel costs you on average sixteen thousand and something in expected losses.

The same session at an American wheel, which Les Ambassadeurs runs, multiplies that by just under two.

The "same game" framing conceals a very significant difference at those stakes.

They achieved, in Doyne Farmer's own words, a twenty percent positive edge over the house on the bets they made using the computer's guidance.

And they made almost no money.

The reason is instructive: every pound not bet using the computer's prediction was still subject to the two point seven percent drain.

Cover bets, misdirection wagers, play before the device was ready, all of it was feeding the house edge at the standard rate.

The physics edge was real.

The accounting was brutal.

The maths worked perfectly on both sides of the ledger.

One more thing that is worth knowing if you are ever offered a rebate programme by a casino host.

If the rebate percentage exceeds the house edge on roulette, you have a positive-expectation game.

That percentage is two point seven percent on European roulette.

Baccarat banker at higher rebate percentages is a different calculation, but that is another lesson entirely.

What the edge gives the casino is certainty over time.

What it gives you, in the short term, is a range of outcomes wide enough to be entertaining and occasionally wonderful.

Just don't confuse the entertainment with an investment thesis.

Keep the maths on your side of the table.

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