Roulette payouts and odds

On a European wheel a single number pays 35 to 1, a split 17 to 1, a street 11 to 1, a corner 8 to 1, a line 5 to 1, a dozen or column 2 to 1 and an even chance 1 to 1. All of them carry the same house edge, 1/37 or 2.70%, because each one pays as if the wheel had 36 pockets instead of 37.

The table is the same at all three of our tables; only the limits change.

Take any bet, multiply the numbers it covers by what it returns per chip (the payout plus your stake), and you always get 36. A number: 1 × 36. A split: 2 × 18. A dozen: 12 × 3. Red: 18 × 2. The wheel, however, has 37 pockets.

So imagine 100 on every one of the 37 numbers. You stake 3,700, exactly one number wins, and it brings back 3,600. You lose 100 every spin without fail — 1/37 of the stake, 2.70%. Any other bet is a slice of that picture, which is why the edge is identical everywhere on the cloth.

The same arithmetic explains “true odds”. A single number has 36 ways to lose and one way to win, so a fair price would be 36 to 1. The table pays 35. The gap between the two, averaged over all spins, is the house’s share.

Roulette payouts are quoted “to 1”: you win that many chips and keep your own. At 35 to 1 a 100 chip earns 3,500, and with your 100 back you hold 3,600. Some sites and machines quote “for 1”, counting the stake inside the number — 36 for 1 is the same deal.

Zero is not a dead pocket you can only lose to. You can back it straight up (35 to 1), in a split with 1, 2 or 3 (17 to 1), in the trios 0–1–2 and 0–2–3 (11 to 1) and in the first four, 0–1–2–3 (8 to 1). These pay exactly like their cousins elsewhere on the layout and carry the same 2.70% edge.

What zero does is beat every outside bet. On 0, red and black, odd and even, both halves, all dozens and all columns lose at our tables. There is no half-back rule.

Most players put down more than one chip. The rule is simple: each bet is paid on its own, and the returns add up. If 17 comes up and you have chips on 17, on the split 17–20 and on black, all three are paid.

Combining bets changes how often you win something and how wide the swings are. It never changes the edge: every chip on the cloth loses 2.70% on average, and the average of a sum is the sum of the averages. A few cases that surprise people:

• Red and black together. 1,000 on each: on any number except zero you get 2,000 back for 2,000, and on zero both lose. You can never win, yet you still lose 2.70% of 2,000 per spin on average — 54 debens.
• Red plus the first four. 1,000 on red and 100 on 0–1–2–3 return something on 20 numbers out of 37 instead of 18, but you finish ahead on the same 18. On 0 and 2 you get back 900 of your 1,100.
• Two dozens. 1,000 each on the first and second cover 24 numbers: +1,000 on any of them, −2,000 on the other 13. You win 65% of spins and still lose 2.70% on average.
• Every number. 100 on all 37 is the cleanest proof there is: −100 every spin, always.

You can build any combination — and see what each number does to it — in the bet calculator.

Many live tables have an oval “racetrack” beside the layout with the numbers in wheel order. It is used for call bets: named sets of ordinary bets that cover a sector of the wheel. Our tables have no racetrack, but every call bet is just splits, corners and numbers, so you can lay one out by hand.

Built from standard bets, they pay standard odds and carry the same 2.70%. Voisins du zéro at 100 per chip, for example, costs 900: on 0, 2 or 3 you collect +1,500, on the other 14 numbers of the sector +900, and on the 20 numbers outside it you lose 900.

French tables sometimes treat zero more gently. Under La Partage an even-money bet loses only half its stake when zero comes up, which halves the edge on those bets to 1/74, about 1.35%. En Prison is a relative: on zero the bet is “imprisoned” for the next spin, and if it wins then, you get your stake back. Its edge is about 1.35–1.39%, depending on what the house does with a second zero in a row.

Neither rule is used in the Rotunda of Shai. On zero an even-money bet loses, and every bet at our table carries the same 2.70%. Inside bets are not covered by these rules anywhere.