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A polished wooden roulette wheel and ivory ball in a candlelit European gaming room.
01The wheel
of fortune

The art ofuncertainty.

A spinning wheel.
A ball that settles into one pocket.

36 numbered pockets.
One zero.

37 pockets.
One winning number.

The wheel of fortune

Who invented
roulette?

Scroll to begin History · Mechanics · Mathematics
Roulette Atlas The origins02 — The inventor mystery
Engraved portrait of Blaise Pascal, 1802.
France · Eighteenth century

Who invented
roulette?

No single inventor has been reliably identified. Casino roulette took shape in eighteenth-century France, well after Pascal’s seventeenth-century work on curves.

1658.Pascal’s
other roulette.

A mathematical curve, not a casino game. In 1658, Pascal’s “roulette” was the cycloid: the curve traced by a point on a wheel rolling along a straight line.

The cycloidA point on a circle rolling to the right without slipping traces an arch. The centre travels a distance r times theta as the circle turns through theta radians. One full turn travels two pi r. One full turn · travel = 2πr (r = radius) The cycloid AB
The red point traces the curveThe wheel rolls without slipping
Imagined reconstruction of a candlelit Parisian gaming salon around 1800, with period dress, a walnut roulette table and tall arches.
Paris · The Palais-Royal

Roulette at the
Palais-Royal.

1802

In an 1802 edition of his novel, Jacques Lablée describes roulette already played at the Palais-Royal: 36 numbers, a red zero and a black double zero.

36 numbers. A red zero. A black double zero.
Two house pockets; 38 pockets in all.

Paris, circa 1800 · Imagined reconstruction
I — FranceScroll ↓01 / 03
Roulette Atlas The zero revolution03 Bad Homburg

Bad Homburg · François & Louis Blanc

One less zero.
Better odds.

By 1843, the Blanc brothers offered single-zero roulette in Bad Homburg, improving players’ odds.

Schematic · 38 pockets → 37 pockets

The second zero
disappears.

All 36 numbered pockets remain.
Removing 00 leaves 37 equal pockets. On modern wheels, the remaining zero is green.

From two zeros to one A schematic 38-pocket wheel loses its double-zero pocket. The remaining sectors expand equally into a 37-pocket European wheel in its standard clockwise number order. Eighteen red numbers and eighteen black numbers remain, alongside one green zero. 0 32 15 19 4 21 2 25 17 34 6 27 13 36 11 30 8 23 10 5 24 16 33 1 20 14 31 9 22 18 29 7 28 12 35 3 26
Single-zero European wheel
House edge

5.26%2.70%

House edge is the casino’s average share of money wagered over many plays. Removing 00 raises each remaining number’s chance from 1/38 to 1/37. With the same 35:1 payout on a single number, the edge falls from 2/38 to 1/37.

38 → 37 pockets2 → 1 house pockets
Two zeros to one18 red numbers · 18 black numbers03
Roulette Atlas The rise of Monte-Carlo04 Monaco
Henry Alford’s nineteenth-century coastal view: the Rock of Monaco across a quiet bay, with terraced hills and Mediterranean vegetation to the east.
Monaco’s eastern coast, in a lithograph published in 1870.

A casino above
the Mediterranean.

Monaco already had a casino in 1856. In 1863, François Blanc took over its gaming enterprise through the Société des Bains de Mer, developing the casino and surrounding resort on the Spélugues plateau.

Plateau des SpéluguesThe future Monte-Carlo
The early casino’s seaward facade, palms and gardens before the rebuilding of 1878; the mountains rise behind its low classical buildings.
The casino’s seaward façade before the rebuilding of 1878.

The Spélugues plateau
becomes Monte-Carlo.

On 1 June 1866, Prince Charles III gave the developing resort its name: Monte-Carlo. The name honours Charles: Monte-Carlo means “Mount Charles”.

Salle Garnier shortly after its 1879 opening: an enormous chandelier, painted ceiling, gilded boxes and the orchestra on stage.
Salle Garnier, shortly after its opening.
Chandelier & painted ceilingPainted proscenium

Salle Garnier.
A theatre by the sea.

Rebuilding began in 1878, adding Charles Garnier’s theatre to the casino complex. Salle Garnier opened on .

1863 — 1879Monaco · Mediterranean coast04
Roulette Atlas / Anatomy of the wheel05
An oblique macro illustration of polished walnut, the brass-edged ball track and central wheelhead, with the numbered ring outside the frame.
The construction

Fixed bowl.
Moving wheelhead.

The ball runs along a raised track fixed to the outer bowl. This track stays still while the ball travels around it.

Walnut, brass & independent motion
The ball slows on the fixed track, encounters a deflector and descends into the rotating numbered wheelhead. 0 32 15 19 4 21 2 25 17 34 6 27 13 36 11 30 8 23 10 5 24 16 33 1 20 14 31 9 22 18 29 7 28 12 35 3 26
Two independent motions

The ball
leaves the track.

The ball travels opposite to the wheelhead. As it loses speed, it drops from the track onto the sloping apron. Fixed deflectors interrupt its path toward the pockets.

The ball circles the fixed track.The ball settles in red 32.

Explore
the wheel.

European roulette wheel, with a stationary bowl and independently rotating wheelheadThirty-seven pockets in the European clockwise sequence. The ivory ball travels on the outer track and passes the fixed deflectors toward the numbered pockets. 0 32 15 19 4 21 2 25 17 34 6 27 13 36 11 30 8 23 10 5 24 16 33 1 20 14 31 9 22 18 29 7 28 12 35 3 26

37 pockets: 36 numbered pockets and one zero.

Roulette Atlas / How to play06 · European roulette

Discover the table

Where every bet begins.

The layout covers 0–36. Inside bets cover one number or a small combination; outside bets cover larger groups.

See the coverage:
Inside: single numbers & small groupsOutside: groups of numbers37 possible outcomes

Swipe the table sideways to reach every betting area →

A single number pays 35:1 Dozens & columns 2:1 · Even-money bets 1:1

Demo units
No real money
Stake 0 units
Choose a chip, then select a betting area.

A winning 1-unit number bet returns 36 units: 35 profit + 1 stake. Net = returned − all stakes. Zero loses on outside bets.

Roulette Atlas / Bets & payouts07 · The geometry of a bet

One border.
Two numbers.

A chip on the border between two cells covers both numbers.

Split: the border between 17 and 20One chip on the shared border covers 17 and 20. Two of 37 outcomes, paying 17 to 1 in profit. 0 1st 122nd 123rd 12 1–18EVENREDBLACKODD19–36 123456789101112131415161718192021222324252627282930313233343536 2 outcomes
Split2numbers covered
Winning bet pays17:1Profit per unit; stake returned
Chance per spin5.41%2 / 37 outcomes

Covered numbers17 · 20On the shared border

Explore the geometryChoose a + marker on the grid to move the bet.

More covered numbers win more often, but pay less. All four bet types have the same 2.70% house edge.

Roulette Atlas / One game, different rules08 · Roulette variants
0 32 15 19 4 21 2 25 17 34 6 27 13 36 11 30 8 23 10 5 24 16 33 1 20 14 31 9 22 18 29 7 28 12 35 3 26
The green 0 is one of 37 equal pockets.
European roulette

One zero.
Thirty-seven pockets.

36 numbered pockets and one green zero. Under standard rules, zero loses an even-money bet.

10 on Red · Zero lands0 returned10 lost · No special zero rule
37pockets

One zero

0

European reference: 37 pockets · one zeroStandard single-zero rules

European 2.70%French · La Partage 1.35%Eligible even-money betsAmerican 5.26%Ordinary betsTriple Zero 7.69%
Scroll to compare
The mathematics of chanceEuropean roulette

One zero. One small difference.

The house keeps
a fraction.

37units wagered

36units returned

97.30%theoretical RTP

A 1-unit Red bet returns 2 units on 18 of 37 outcomes, and nothing on the other 19. Weight every possible outcome equally: 37 units wagered, 36 returned.

The difference is 1 / 37: a 2.70% house edge. This is an expectation, not a prediction for 37 actual spins.

RTP includes returned stakes. Individual sessions can return more, less, or nothing.

Roulette Atlas / The mathematics of chance09 · RTP & house edge

97.30% is not
a promise.

A 1-unit bet on Red returns 2 units or nothing. Return to player (RTP) is the average share of stakes returned, including winning stakes.

Red18 winning pockets · 2 units returned per win
Straight-up 171 winning pocket · 36 units returned per win
Red · actual RTPTheoretical RTP · 97.30%Sample 01
Full history
Full history
Every spin
Results from one European roulette outcome sequence. Both bets use the same outcomes.
Latest spins
    Red returns 2 · Black or zero returns 0

    1,000 spins · 1,000 units staked on each bet

    18 winning pockets
    2 units returned per win

    105.00%Actual RTP

    1,050 returned+50 net

    1 winning pocket
    36 units returned per win

    90.00%Actual RTP

    900 returned−100 net

    Theoretical RTP97.30%36 / 37 · either bet
    Actual RTP · RedReturned ÷ staked × 100
    —
    Spins
    —
    Units staked
    —
    Units returned
    —
    Net result
    —
    Spins

    The expected return is not a guaranteed result.

    As more spins accumulate, the observed average can move closer to theory, but no finite sample is guaranteed to match it. Red and 17 have the same theoretical return; their fluctuations can be very different.

    Roulette Atlas / Strategies & myths10 · Can you beat the wheel?

    Double after
    a loss.

    Martingale doubles the next even-money bet after each loss. A later win can recover the stakes and leave a 1-unit profit — if the next wager is affordable.

    Example: a 1-unit Red bet, doubled after each loss.

    1LOSS · 1 lost2LOSS · 2 lost4LOSS · 4 lost8WIN · 16 returned
    15 staked→16 returned=+1 net result

    A win resets the next stake to 1. Recovery depends on reaching that win.

    The next bet
    becomes the problem.

    Seven consecutive losses consume all 127 units. The next required bet is 128 — twice the table maximum, with no bankroll left to place it.

    Seven losses · Starting bankroll: 127 units · Table maximum: 64

    1loss 12loss 24loss 38loss 416loss 532loss 664loss 7 REQUIRED · NOT WAGERED 128 NO BET CAN BE PLACED 0 available · 64 maximum 64 was allowed

    127units lost

    0bankroll remaining

    The wheel's odds never changed.
    The required stake outgrew the available money.

    Six blacks.
    Is red next?

    On an ideal fair wheel, spins are independent. The last six results do not change the probability of Red, Black or Zero on the next spin.

      ?Next spin

      Different history.
      Same next-spin probabilities.

      Red48.65%18 / 37
      Black48.65%18 / 37
      Zero2.70%1 / 37

      The stakes change.
      The odds don't.

      Flat betting keeps the stake at 1. Martingale doubles after a loss and resets after a win. Neither changes the wheel's probabilities or its house edge.

      Example: seven consecutive losses.1 unit per chip · 127 starting units · 64 maximum

      Stakes in units · fixed at 1

      Total wagered
      0
      Bankroll left
      127
      Net result
      0

      Stakes in units · double after a loss

      Total wagered
      0
      Bankroll left
      127
      Net result
      0

      Martingalenext stake128

      Stopped: next stake 128 exceeds the bankroll and table maximum.

      Expected loss = 1 / 37 × expected total wagered. The 2.70% edge applies to wagered volume, not the starting bankroll or an exact session loss.

      Fibonacci uses stakes from the sequence 1, 1, 2, 3, 5, 8…; each new term adds the previous two.D’Alembert commonly adds one unit after a loss and subtracts one after a win.

      Roulette Atlas / Beyond the traditional table11 · Modern roulette
      Illustrated studio camera aimed toward a physical roulette wheel, with a dealer in the background.

      The table
      goes live.

      A real wheel. A human dealer. Live video carries the action to players who place their bets through a digital interface.

      Camera → live video
      The result still comes from the wheel.

      Remote player Red · 1 virtual unitDigital bet, physical outcome
      Physical wheel→Live video→Digital bets

      Faster rounds.
      Different equipment.

      Speed changes the pace. Automation changes what launches the ball. Both can use a physical roulette wheel.

      Illustrated live dealer beside a physical roulette wheel.Illustrated equipment: a covered physical roulette wheel with a mechanical ball launcher.
      Human dealer
      Physical ball launch
      ≈25seconds per round

      Evolution Speed Roulette — approximately 25 seconds per round. This timing is specific to that product; faster play alone does not change the payouts.

      Bets close→Ball launched→Physical result

      Illustrated unbranded studio with a roulette wheel and illuminated tabletop.

      When the
      payout changes.

      Evolution Lightning Roulette adds Lucky Numbers to a live single-zero wheel. The trade-off: ordinary straight-up wins pay 29:1 instead of 35:1.

      Example: 1 unit on 17

      1518211417120131619

      1 unit on 17Straight-up · one number

      Lucky Numbers
      350x17100x29200x
      Assigned Lucky Payout on 17100x

      Winning number 17

      100 units returned +99 net

      A 100x payout returns 100 times the stake: 100 units in total, including the original unit.

      Standard · straight-up win35:1+35 net · 36 total returned

      Lightning · no multiplier29:1+29 net · 30 total returned

      If Lucky 17 wins · example100x+99 net · 100 total returned

      1–5 Lucky Numbers per round · 50x–500x Lucky Payouts.
      Other standard bet categories retain their usual payouts.

      Macro illustration of a physical ball track and dual-feed launch assembly, without an exact manufacturer layout. Ball 1Ball 2

      One wheel.
      Two winning numbers.

      Evolution Double Ball sends two balls from a dealer-triggered launch device. One round produces two results, with specialty bets and settlement rules.

      Ball 1 →17

      Ball 2 →32

      Two results do not mean ordinary bets simply pay twice. The game’s own settlement rules apply.

      Live / AutoPhysical wheel

      ≠

      RNG rouletteSoftware-generated result

      Example round: two balls, two winning numbers.

      Where the result comes from.

      A dealer or an automated launcher can operate a physical wheel. RNG roulette generates its result in software.

      Illustrated live studio.
      Live DealerPhysical-wheel outcome

      A human dealer. A physical wheel.

      Betting closes before the ball settles; the live feed carries the result.

      Players bet remotely using the rules and limits of the selected table.

      Payouts, available bets and limits depend on the specific product. A format name alone does not define its RTP.

      Roulette Atlas / Ways to play11 · Beyond the traditional table

      In person.
      Or online.

      At a casino table or in live online roulette, a physical wheel determines the result. RNG roulette uses software. The betting procedure and available rules depend on the game.

      Illustration of a physical roulette table with walnut wheel, chips and dealer
      Illustration · Physical table

      The dealer. The felt. Your chips.

      Place chips on the felt while betting is open. The dealer runs the round, closes betting and pays winning bets after the ball lands.

      Result
      Physical wheel
      Wager
      Physical chips

      Some casinos use a different chip colour for each player. Confirm the value of your chips with the dealer.

      Physical table
      Roulette Atlas / The final spin12 · One wheel. One outcome.
      European roulette wheel, with a stationary bowl and independently rotating wheelheadThirty-seven pockets in the standard European clockwise sequence. The outer bowl is stationary; the numbered wheelhead and ball move independently. 0 32 15 19 4 21 2 25 17 34 6 27 13 36 11 30 8 23 10 5 24 16 33 1 20 14 31 9 22 18 29 7 28 12 35 3 26

      Thirty-seven
      possibilities.

      On a European roulette wheel, the ball can finish in any of 37 pockets: numbers 1–36 and a single zero.

      1 / 37The chance of any one pocket
      on an ideal, fair wheel.

      One spin.
      One result.

      Choose what to examine,
      then spin the wheel.

      Each spin generates an independent result.

      The pocket determines the outcome.
      The bet determines the return.

      European roulette · 36 numbers + one zero

      Menu