A standard European roulette wheel has 37 pockets: numbers 1 through 36 and one zero. Most ordinary wagers carry the same house edge:
[ H=\frac{1}{37}=0.027027\ldots=2.7027% ]
The edge is not created because zero is “more likely” than another pocket. Every pocket has the same theoretical probability on a balanced wheel. The edge appears because standard payouts are one unit short of fair odds for a 37-pocket game.
The straight-up bet shows the whole mechanism
A one-number wager wins on 1 pocket and loses on 36. European roulette normally pays 35 to 1 rather than the fair 36 to 1.
For a one-unit straight-up bet:
[ EV=\frac{1}{37}(35)-\frac{36}{37}(1)=-\frac{1}{37} ]
Expected value is therefore -0.027027 units per unit wagered. The player’s theoretical return is 97.2973%, and the casino’s theoretical edge is 2.7027%.
This does not mean a player loses 2.70% on every spin. A straight-up bet usually loses one unit and occasionally wins 35 units. The percentage appears only as the average of many comparable wagers.
Why standard bets share the same 2.7027% edge
Let:
- (c) = number of pockets covered;
- (p) = net payout in units to one;
- 37 = total pockets.
The expected value of a one-unit wager is:
[ EV=\frac{c}{37}p-\frac{37-c}{37} ]
Standard payouts are arranged so this expression equals (-1/37) for the main roulette wagers.
| Bet | Pockets covered | Net payout | Win probability | House edge |
|---|---|---|---|---|
| Straight up | 1 | 35 to 1 | 1/37 = 2.7027% | 2.7027% |
| Split | 2 | 17 to 1 | 2/37 = 5.4054% | 2.7027% |
| Street or zero trio | 3 | 11 to 1 | 3/37 = 8.1081% | 2.7027% |
| Corner | 4 | 8 to 1 | 4/37 = 10.8108% | 2.7027% |
| Six line | 6 | 5 to 1 | 6/37 = 16.2162% | 2.7027% |
| Dozen or column | 12 | 2 to 1 | 12/37 = 32.4324% | 2.7027% |
| Red/black, odd/even, low/high | 18 | 1 to 1 | 18/37 = 48.6486% | 2.7027% |
Hit frequency changes dramatically across this table, but price does not. An even-money bet wins far more often than a straight-up number; it also pays far less when it wins.
The roulette payouts guide explains profit, returned stake, and overlapping settlements in more detail.
A direct even-money calculation
Consider one unit on red. There are 18 red pockets, 18 black pockets, and one green zero.
[ EV=\frac{18}{37}(1)-\frac{19}{37}(1)=-\frac{1}{37} ]
The extra losing outcome is zero. Betting black, odd, even, 1–18, or 19–36 produces the same standard calculation.
Covering both sides does not remove the edge. One unit on red and one unit on black creates a two-unit package:
- on any nonzero number, one side wins and the other loses, producing zero net result;
- on zero, both units lose.
The package loses two units on 1 of 37 spins, so expected loss is (2/37). Dividing by the two units wagered still produces a 2.7027% house edge.
Call bets and wheel sections do not receive a special discount
European layouts may offer neighbors, tiers, orphelins, voisins du zéro, zero spiel, and other announced combinations. These are packages of individual straight, split, trio, or corner chips. When every component uses standard payouts, the package normally retains the same 2.7027% edge.
The package can have a different hit rate and a very different result distribution. A voisins wager covers many pockets and wins more frequently than one straight-up number, but the expected cost remains the sum of the component wagers’ expected costs.
The player should still verify the exact chip count and placement. Two casinos can use similar call-bet names while requiring different total units or applying different table procedures.
La Partage and En Prison are genuine exceptions
Some single-zero tables protect even-money bets when zero appears.
Under La Partage, half of a qualifying even-money stake is returned and half is lost. The expected loss on zero becomes half a unit rather than one full unit:
[ H_{partage}=\frac{0.5}{37}=1.35135% ]
An economically equivalent En Prison rule can produce a similar long-run edge, but the exact treatment of a second zero and subsequent settlement must be confirmed. These rules normally apply only to red/black, odd/even, and low/high, not to inside bets, dozens, columns, or call-bet packages.
Read La Partage procedure and En Prison procedure before treating a French-style table as a 1.35% game.
European and French roulette are not automatic synonyms
“European roulette” usually identifies the 37-pocket, single-zero wheel. “French roulette” may also refer to a French-language layout, call-bet structure, and player-favorable zero rules. A European single-zero table without La Partage or En Prison remains a standard 2.7027% game.
The label on a game tile, cabinet, or table sign is not enough. Confirm:
- the number of zero pockets;
- the exact payout table;
- whether a zero-protection rule exists;
- which wagers qualify;
- minimums for inside, outside, and announced bets.
Published table-game rules provide a useful settlement baseline. The Massachusetts Gaming Commission’s roulette rules list standard wager types and payout odds, but every player must follow the rules posted for the actual table and jurisdiction.
Table minimum can outweigh the lower percentage
Choosing the lower-edge wheel is usually correct when stakes are comparable. But expected loss is measured in money, not percentages alone.
For one spin:
[ EL=Bet\times House\ edge ]
Compare a $10 American table with a $20 European table:
| Table | Bet | Edge | Expected loss per spin |
|---|---|---|---|
| American double-zero | $10 | 5.2632% | $0.5263 |
| European single-zero | $20 | 2.7027% | $0.5405 |
The European game has the better price per dollar, but the required stake is twice as large, producing slightly more expected loss per spin.
The break-even European stake relative to an American stake is:
[ \frac{B_E}{B_A}=\frac{2/38}{1/37}=1.9474 ]
A European wager below about 1.947 times the American wager has lower expected loss per spin. Above that ratio, the lower edge may be offset by the higher minimum.
This does not make the American wheel better. It shows why game selection and bet sizing must be evaluated together. The European-versus-American comparison applies this tradeoff across common bet types.
Session cost depends on total action
A player making 120 spins at $5 per spin creates:
[ A=120\times$5=$600 ]
At the standard European edge:
[ EL=$600\times\frac{1}{37}=$16.22 ]
At a qualifying La Partage even-money table, the same action would have theoretical loss of about $8.11.
Actual results can be far from either number. Straight-up and small-cover bets have much higher variance than even-money bets, even though both share the standard 2.7027% price. House edge measures average cost; variance describes how widely the session can move around that average.
Several chips on one layout still have one combined expected cost
Players often spread chips across inside and outside bets, then try to identify one “main” house edge. The clean method is to calculate expected loss for each component and add the results.
Suppose one spin contains:
- $2 on a straight number;
- $4 on a street;
- $10 on red.
All three are standard single-zero wagers at 1/37 house edge, so total action is $16 and expected loss is:
[ EL=$16\times rac{1}{37}=$0.4324 ]
The bets can overlap. If the ball lands on a red number inside the chosen street, more than one component wins. That changes the possible settlement amounts, but it does not change the sum of the components’ expected values.
A side bet or proprietary wager with a different payout must be calculated separately. Do not apply 2.7027% automatically to a bet merely because it appears on a European roulette terminal. The standard edge depends on standard coverage and payouts.
RTP, hit rate, variance, and table hold answer different questions
The standard theoretical return is:
[ RTP=1-H=1- rac{1}{37}=97.2973% ]
That figure is based on total wagers. It does not state how frequently a bet wins or how smooth a session will be.
- Hit rate is the chance that a particular wager wins on one spin.
- House edge is expected loss divided by amount wagered.
- Variance describes the spread of possible results around expectation.
- Table hold is an operational ratio based on casino win relative to buy-ins or drop over a reporting period.
A straight-up player and an even-money player can both face 2.7027% house edge while experiencing radically different session paths. The straight-up player loses frequently and occasionally receives a large award. The even-money player wins nearly half of spins and moves in smaller increments.
Table hold can also be negative on a particular shift if players win more than they bought in for. That does not mean the mathematical house edge changed. Hold is affected by buy-ins, cash-outs, credit, time played, bet mix, and short-run luck.
Wheel order does not change standard bet pricing
The European wheel sequence is arranged differently from the American sequence, and neighboring-number bets depend on that physical order. The standard house edge still comes from 37 pockets and the payout schedule. Moving numbers around the rim does not alter the probability of a single pocket on a balanced wheel.
Wheel order matters for identifying neighbors and announced sectors, not for turning recent results into a forecast. A number appearing several times remains one of 37 possible outcomes on the next independent spin. The edge calculation does not include a term for the previous result.
A lower edge improves cost, not the chance of finishing ahead
A 2.7027% edge is materially better than 5.2632%, but either game can produce a winning session. House edge does not equal the probability that the casino wins every visit.
For example, one $10 red bet has a 48.6486% chance to win $10, a 51.3514% chance to lose $10, and expected loss of about $0.2703. Over many spins, the distribution depends on the order of wins and losses. A player may finish ahead after 20 spins even though each wager had negative expected value.
Increasing spin count does not make a session’s result equal the exact theoretical percentage. It increases total exposure and gives the average result more opportunity to move toward expectation relative to total action. The bankroll can be exhausted long before that convergence becomes visible.
A practical European-wheel check
Before placing a bet:
- count the green pockets and confirm there is no double zero;
- inspect the payout and rules display;
- identify any La Partage or En Prison treatment;
- compare the minimum with nearby alternatives;
- decide the total stake and number of spins before play begins.
Use the roulette odds calculator to check coverage and payouts. Use the expected-loss calculator to compare stake, pace, and session length. A single-zero wheel improves the price, but it does not make a negative-expectation game profitable or protect a bankroll from short-run swings.