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The Martingale Strategy Explained with Real Numbers
The Martingale betting system with exact numbers: streak odds, bust risk over 100 series, expected value, and a Fibonacci comparison.
October 25, 2026
Photo: Pavel Danilyuk / Pexels
Roulette rules, all bet types and payouts, worked examples, and the maths behind the 2.70% and 5.26% house edge on European and American wheels.
To play roulette, you place chips on numbers or groups of numbers, the dealer spins a ball around a numbered wheel, and every bet covering the winning pocket is paid at fixed odds, from 1:1 on red or black to 35:1 on one number.
Roulette uses a wheel with 37 pockets (European, 0 to 36) or 38 pockets (American, with an extra 00). Players bet on single numbers, small groups or outside bets such as red, odd or a dozen. Payouts are fixed, so the house edge comes from the zero pockets: 2.70% on a European wheel, 5.26% on an American wheel and 7.89% on the American five-number bet. French tables with La Partage cut the even-money edge to 1.35%. Wheel choice matters more than bet choice.
Roulette rules fit in one sentence: players place chips during the betting window, the dealer calls “no more bets”, the ball settles in one pocket, losing chips are swept away and winners are paid at the posted odds. No player decision affects the spin.
Every round follows the same order. We call it the 5-step round:
Live online tables use the same sequence with a countdown timer, as a live roulette rules sheet filed with the Nevada Gaming Control Board shows.
The European wheel has 37 pockets (0 to 36), the American wheel has 38 pockets (0, 00 and 1 to 36), and French roulette uses the European wheel plus La Partage or En Prison rules on even-money bets. Zeros set the house edge.
| Wheel | Pockets | Green pockets | House edge |
|---|---|---|---|
| European (single zero) | 37 | 0 | 2.70% on every bet |
| French (single zero + La Partage) | 37 | 0 | 1.35% on even-money bets, 2.70% on the rest |
| American (double zero) | 38 | 0, 00 | 5.26%; five-number bet 7.89% |
| Triple zero | 39 | 0, 00, logo pocket | 7.69% on every bet |
The maths is short. A straight-up bet on a European wheel wins 35 units with probability 1/37 and loses 1 unit with probability 36/37. Expected value = (35 − 36) ÷ 37 = −1/37 = −2.70% of the stake. On an American wheel the same bet gives (35 − 37) ÷ 38 = −2/38 = −5.26%. The American five-number bet (0, 00, 1, 2, 3) pays 6:1: (5 × 6 − 33) ÷ 38 = −3/38 = −7.89%.
Both wheels carry 18 red and 18 black numbers; zeros are green. François and Louis Blanc introduced the single-zero wheel in Bad Homburg in 1843. La Partage returns half of an even-money stake when zero hits.
Roulette bets split into inside bets on specific numbers (straight, split, street, corner, six line) and outside bets on large groups (dozens, columns, red or black, odd or even, high or low). Payouts run from 35:1 for one number to 1:1 for 18 numbers.
| Bet | Numbers covered | Payout | Win chance (European) | Win chance (American) |
|---|---|---|---|---|
| Straight | 1 | 35:1 | 2.70% | 2.63% |
| Split | 2 | 17:1 | 5.41% | 5.26% |
| Street | 3 | 11:1 | 8.11% | 7.89% |
| Corner | 4 | 8:1 | 10.81% | 10.53% |
| Six line | 6 | 5:1 | 16.22% | 15.79% |
| Dozen or column | 12 | 2:1 | 32.43% | 31.58% |
| Red/black, odd/even, 1–18/19–36 | 18 | 1:1 | 48.65% | 47.37% |
One formula produces every payout in the table: payout = (36 ÷ numbers covered) − 1. A street covers 3 numbers, so 36 ÷ 3 − 1 = 11, and the street pays 11:1. European call bets (voisins du zéro: 17 numbers, tiers: 12, orphelins: 8) are bundles of ordinary splits and corners, so they carry the same 2.70% edge.
A roulette payout equals the stake multiplied by the posted odds, and the winning stake is returned on top. A $10 straight-up win pays $350 plus the $10 stake. A $10 win on red pays $10 plus the stake. The house keeps losing chips.
Worked example on a European wheel with $40 on the layout:
| Bet | Stake | If the ball lands on 17 | If the ball lands on 0 |
|---|---|---|---|
| Straight on 17 | $10 | +$350 | −$10 |
| Split 17/20 | $10 | +$170 | −$10 |
| Red | $20 | −$20 (17 is black) | −$20 (−$10 with La Partage) |
| Net result | $40 | +$500 | −$40 (−$30 with La Partage) |
Over many spins, the $40 layout costs $40 × 2.70% = $1.08 per spin on average. Single results swing far around that figure; the cost stays fixed. Test other layouts with our house edge calculator.
The payout formula (36 ÷ numbers covered) − 1 explains why every standard bet on a single-zero wheel costs the same 2.70%. The casino pays as if the wheel had 36 pockets, while the wheel has 37. Mixing inside and outside bets changes how volatile a session feels, not what it costs per unit staked. The one standard exception is the American five-number bet: the formula gives 6.2:1, the table pays 6:1, and the edge rises to 7.89%.
Online roulette comes in two forms: RNG roulette, where certified software selects the pocket, and live roulette, where a studio dealer spins a physical wheel on video. Both use the same layout, bets and payouts, so the wheel type still sets the house edge.
Before the first spin, use the 3-check method:
Roulette is entertainment, not income; our responsible gambling page lists tools and help lines.
Real-money online roulette is legal only where national or state law allows it; in the US, only in states that license online casinos. In India, the Promotion and Regulation of Online Gaming Act, passed by Parliament on 20 and 21 August 2025, bans offering online money games. Offering them can bring up to 3 years in prison and a ₹1 crore fine (as of October 2026). Gambling Hero does not encourage play in India; see our India legal guide for the current position.
No roulette bet or betting pattern changes the house edge, but table choice does: a single-zero wheel costs 2.70%, a French table with La Partage costs 1.35% on even-money bets, and an American wheel costs 5.26% of every stake.
| Table | 100 spins × $10 on red | Expected loss |
|---|---|---|
| French, La Partage | $1,000 wagered | $13.50 |
| European | $1,000 wagered | $27.00 |
| American | $1,000 wagered | $52.60 |
Betting systems reshape results but leave the cost per unit staked unchanged; see roulette strategy and martingale strategy. For other games, read Which Casino Games Have the Best Odds? and our roulette odds guide.
Roulette is one of the easiest casino games to learn. One formula gives every payout, and one number, the count of zeros, gives the price. Because the rules are short, players look for complexity in betting patterns, and patterns change nothing. Our editorial view: learn the 7 bet types, pick a single-zero wheel, prefer La Partage, and skip American tables when a European one is available. Treat the 2.70% as an entertainment fee and fix the session budget before the first chip goes down.
Neither. Zero loses every even-money bet; La Partage returns half the stake.
It is the French dealer call for “no more bets”.
Even-money bets win 48.65% of European spins, at the same 2.70% edge as a straight-up bet.
Offering online money games is banned under the Act passed in August 2025. Check our India legal guide.