ACT I · THE BIRTH OF ROULETTE
Every spin has a story.
Roulette means “little wheel” in French. But this little wheel has a remarkable past.
A disputed inventor. A game that crossed the Atlantic. And one missing zero that changed the odds.
The wheel turns. The ball travels the other way.
THE ORIGINS · FRANCE, 18TH CENTURY
Who invented roulette?
The surprising truth: nobody knows for certain.
Roulette began taking its familiar form in France during the 18th century, but its original inventor remains unknown.
1658 · PASCAL’S MATHEMATICAL WORK
Why Pascal gets the credit
The game is often credited to the French mathematician Blaise Pascal. But there’s a catch.
In 1658, Pascal published a work called Histoire de la roulette. Despite its name, it was about geometry, not gambling.
Pascal was studying a cycloid: the curve traced by a point on the edge of a circle as it rolls along a straight line. Imagine a dot of paint on a bicycle tyre and follow the arch it draws as the wheel rolls.
Follow the red dot. The arch it draws is a cycloid.
A closer look
THE ORIGINS · FRANCE, 18TH CENTURY
“Roulette” was also a name for the cycloid. Pascal studied its geometry and published work on it in 1658. That establishes what this document discusses. It does not establish that he invented the casino game. The distinction matters when a familiar origin story is repeated as fact.
There is no reliable historical evidence that Pascal invented the casino game.
To follow the game itself, we have to leave Pascal’s study and step into the gaming rooms of eighteenth-century France.
FRANCE · 18TH CENTURY
All eyes on the ball.
Leave Pascal’s geometry behind and step into a gaming room. Here, the question is much simpler: where will the ball stop?
During the eighteenth century, roulette took its familiar form in France. A wheel, a ball and a table of bets turned a single moment of uncertainty into a shared spectacle.
The wheel: The ball settles in one numbered compartment, called a pocket. That is the winning result.
The bets: Players choose what to back before the result: a number, a colour or another group of numbers.
The players: One ball gives everyone at the table the same result. Each person’s bet decides what that result means for them.
An imagined French gaming room · Late 18th century
A game with a story of its own.
By 1802, roulette was the title of a novel by the French writer Jacques Lablée. Its subtitle means “the story of a gambler”.
About the book
Jacques Lablée · La roulette, ou Histoire d’un joueur · Paris edition, 1802
The title translates as “Roulette, or the story of a gambler.” The edition identified here was published in Paris in 1802. It gives us a literary object from the period. Its publication date is not the date roulette was invented, and this room is an artistic reconstruction.
HOMBURG · 19TH CENTURY
One less zero. A different game.
The smallest change on the wheel made a measurable difference.
In 1841, twin brothers François and Louis Blanc opened a casino in Homburg, a German spa town. Their licence came with a deal: build a spa house and an English-style park.
Pocket-count comparison · Not a reconstruction of a nineteenth-century wheel.
François became closely associated with single-zero roulette: a wheel with one zero instead of both 0 and 00.
Remove the extra zero and a bet on a number from 1 to 36 has one fewer way to lose. The winning payout stays the same.
The house edge—the casino’s average share of money wagered over many bets—falls from 5.26% to 2.70% in this comparison.
A smaller house edge gives the player better odds, but the casino still has an advantage. It does not make the next spin predictable.
Single-number bet · 35:1 profit payout · Equally likely pockets
How the numbers work
HOMBURG · 19TH CENTURY
A winning 1-unit bet pays 35 units in profit and returns the original stake: 36 units in total. With 38 equally likely pockets, its average return is 36/38 of the stake. With 37, it is 36/37. The difference is the house edge. These are long-run averages for this bet, not a prediction for one spin.
MONACO · 1863–1879
A place worth the journey.
François Blanc’s next venture lay on the Mediterranean. In 1863, he took charge of the Société des Bains de Mer, the company developing Monaco’s casino resort.
The ambition reached beyond the gaming table: hotels, gardens and entertainment would give visitors reasons to arrive—and to stay.
1863 · The venture begins
Prince Charles III’s new company brings François Blanc to Monaco.
1866 · A name for the dream
On 1 June, the district receives the name Monte-Carlo.
1879 · The curtain rises
Architect Charles Garnier’s theatre opens, with actress Sarah Bernhardt at its inauguration.
Elsewhere, earlier…
NEW ORLEANS · 1835
Meanwhile, across the Atlantic.
Before Monte-Carlo had a name, roulette was already being described on the other side of the ocean.
In his 1835 travel book, Joseph Holt Ingraham takes us into a New Orleans gambling room: silver clinks, players call out, and a small ball rattles around a wheel.
“in one a single cipher, in the other two ciphers”
J. H. Ingraham · The South-West · 1835
Read the 1835 description
J. H. Ingraham · The South-West, Volume I · 1835
Ingraham describes “two squares additional, in one a single cipher, in the other two ciphers”. Here, “cipher” means zero. This is evidence of a double-zero wheel in his account of New Orleans. It does not tell us when roulette first arrived in America or what every American table looked like.
Cipher meant zero. His description includes numbers 1 to 36, plus 0 and 00. It is a glimpse of one table, not a date for the game’s first arrival in America.
Pocket-count diagrams · 1–36, with one zero or two
The story has branches.
Now look inside the wheel.ACT II · INSIDE THE WHEEL
Take the wheel apart.
What actually happens inside a roulette wheel?
The numbered disc spins inside a stationary wooden bowl. Meanwhile, a small ball travels around the outer track in the opposite direction. As the ball slows down, it drops toward the spinning numbers, bounces off obstacles and eventually lands in a pocket.
Take the wheel apart to see how it all works.
Single-zero study model · one design, seen layer by layer
01 · The bowl
The bowl is the fixed outer body. Its raised circular track carries the ball during the opening laps; the slope beneath leads towards the numbered disc.
02 · The rotor
The rotor is the inner disc that turns around the central spindle. The numbers and their pockets move together, while the outer bowl stays still.
03 · The pockets
A pocket is a small compartment that can hold the ball. Thin dividers separate neighbouring pockets. The number beside the pocket where the ball finally stays is the result.
A small obstacle. A big change of direction.
The raised bumps on the slope are deflectors: obstacles that interrupt the ball’s smooth path. A collision can send it bouncing towards the moving pockets.
The numbers have neighbours. Just not the ones you expect.
On this single-zero wheel, 0 sits between 26 and 32. Follow the ring and you will not count from 1 to 36. Its 37 places hold 18 red numbers, 18 black numbers and one green zero.
This is one conventional single-zero design. Real wheels vary: even the angle of the ball track and the depth of the pockets can differ between models.
07 · THE PHYSICS OF THE SPIN
A spin is a journey.
Two directions. One eventual resting place.
The dealer sends the ball around the outer track, opposite the spinning rotor. Follow it from the fast opening laps to the final bounce.
Illustrative motion · timing and bounces simplified
01 · Launch
The ball follows the circular track while the rotor turns the other way. The track keeps bending the ball’s path into a circle; the ball gradually loses speed.
02 · Descent
Once the ball is too slow to keep circling high on the track, it rolls down the sloping bowl under gravity. The rotor is still turning underneath.
03 · Deflection
A deflector or a pocket divider can change the ball’s direction. It may touch a pocket, bounce out and cross into another. The first contact is not the finish.
04 · Settle
Eventually the ball stays in one pocket and travels with the rotor. It has stopped moving relative to that pocket, even though the whole disc may still be turning.
Why watching is easier than predicting.
The ball’s starting speed, the rotor’s speed and the points of impact all matter. A small change can bring a different pocket under the ball when it arrives. Physics describes the motion; a short animation cannot predict a real spin.
Now you know the wheel. Next comes the table.
In the next chapter: where bets go, what the dealer calls and how to read a result.
ACT III · MASTER THE GAME
Your first spin.
The wheel gives one answer. Your chip decides which question you ask.
- 1 · Choose a table
- 2 · Choose a chip
- 3 · Place a bet
- 4 · No more bets
- 5 · Read the result
A guided round · practice chips
One zero. Thirty-seven answers.
Find the green 0. Our practice table covers 0–36 and accepts 1–100 units per round.
Teaching example · the result is chosen to explain the payout.
0–36
01 · Read the table first.
Start with the zeros and the limits. A single-zero table has 37 possible results: 0 to 36. Check the minimum and maximum stakes before choosing a chip; limits can differ between bets. Here, you have 100 practice units and an ordinary single-zero table.
02 · Give the chip a value.
At many live tables, each player receives a different colour of roulette chip so the dealer can tell their bets apart. Agree the value before playing: the same-looking chip can represent different amounts. Here, one chip is worth 5 practice units.
03 · Ask a question with your bet.
Place one 5-unit chip on red and you are asking: will the ball land on any red number? That covers 18 of the 37 pockets. You do not need to name the exact number, but a black number or zero will lose this bet.
04 · “No more bets.”
The dealer can start the ball while bets are still open. Once “no more bets” is announced, stop adding, moving or removing chips. The ball keeps travelling, but your choices for that round are fixed.
05 · Read the return, not just the win.
Our teaching round finishes on 32, a red number. Your 5-unit stake wins 5 units and the original stake comes back too: 10 units returned in total. Had the ball landed on 17 or 0, nothing would come back under these ordinary rules.
09 · THE ART OF BETTING
A chip changes everything.
On a number. Between two. At the meeting of four. A few millimetres change the bet.
Choose a chip, then click a number. Hover or focus to see what it covers.
Your table is open.
Choose a chip and place your first bet. No money is used.
Your placed bets will appear here.
Explore a particular result
This chooses the result for learning. “Spin the wheel” makes a fresh random draw instead.
European single zero · 1–100 units per round · ordinary zero rule · 100 starting units · no cash value
The table is a map of possibilities.
Inside bets sit on the numbered grid. A straight bet covers one number; a split covers two touching boxes. A street covers a row of three, a corner covers four adjoining numbers, and a six line covers two neighbouring rows. Select a type above to reveal its exact chip positions.
Outside bets sit around the grid. A dozen covers 1–12, 13–24 or 25–36. A column follows every third number, such as 1, 4, 7 and so on. Red/black, odd/even and low/high each cover 18 numbers. None of these outside bets includes zero.
More ways to win. A smaller payout.
A single number has one winning outcome out of 37 and pays 35 to 1 in profit. A corner has four winning outcomes and pays 8 to 1. You hit more often by covering more numbers, but the reward per chip is smaller.
On this ordinary single-zero table, every bet in the guide has the same expected loss per unit staked: 1/37, about 2.70%. Changing the shape of the bet changes how often and how much you win. It does not remove the casino’s mathematical advantage.
A winning bet can sit in a losing round.
Put 1 unit on 17 and 40 units on red. The ball lands on 17, which is black. Your number bet wins and returns 36 units, but the red bet loses. You staked 41 units altogether, so the whole round ends 5 units down. A winning bet is only part of the story: compare everything returned with everything you put on the table.
| Bet | Numbers | Chance | Profit | Returned |
|---|---|---|---|---|
| Straight | 1 | 2.70% | 35:1 | 36 |
| Split | 2 | 5.41% | 17:1 | 18 |
| Street | 3 | 8.11% | 11:1 | 12 |
| Corner | 4 | 10.81% | 8:1 | 9 |
| Six line | 6 | 16.22% | 5:1 | 6 |
| Dozen | 12 | 32.43% | 2:1 | 3 |
| Column | 12 | 32.43% | 2:1 | 3 |
| Even money | 18 | 48.65% | 1:1 | 2 |
| Zero trio | 3 | 8.11% | 11:1 | 12 |
| First four | 4 | 10.81% | 8:1 | 9 |
Amounts are in units. Profit excludes the original stake. Returned includes it. Probabilities assume a fair 37-pocket wheel.
10 · BEYOND THE BASICS
Neighbours, in another order.
The table counts upward. The wheel does not. Follow a sector and watch its bets appear.
From wheel to table.
Each mark shows the units staked on that position.
A name can place a whole group of chips.
Think of a sector name as an instruction to place several bets at once. With 1-unit chips, Voisins du Zéro (“neighbours of zero”) costs nine units and covers 17 numbers. Tiers du Cylindre costs six for 12 numbers on the opposite side. Orphelins, the “orphans”, costs five for the eight numbers left over. The layout below shows where every unit goes.
A Neighbours bet starts with a number you choose. Here it places one 1-unit chip on that number and one on each of the two pockets on either side. Choose 0 and the five numbers are 3, 26, 0, 32 and 15. They are neighbours on the wheel, even though they are far apart on the table.
Seventeen has a surprise.
In Orphelins, 17 belongs to two splits: 14/17 and 17/20. If 17 lands, both win. With one unit on each position, the five-unit group returns 36 units. If 6 lands, only the 6/9 split wins and the same group returns 18. This is why the group summary gives a range, while the receipt checks each bet separately.
When zero changes
the rules.
Red and black look like two halves of a wheel, until you notice the green zero. Under ordinary rules, a red bet loses when zero lands. Some tables soften that loss for even-money bets: red/black, odd/even and low/high, which normally pay one chip of profit for each chip staked.
The same 10-unit bet on red
The 10 units are lost. Zero is neither red nor black.
Now choose a non-zero result:
This example resolves En Prison with a non-zero result. Repeated-zero rules vary; check the table before you play.
La Partage · half comes back.
With La Partage, zero returns half an eligible stake immediately. Put ten units on red and zero returns five. The rule does not protect a dozen, a column or a bet on individual numbers. On a fair single-zero wheel it reduces the expected loss on eligible bets to about 1.35% of the stake.
En Prison · the stake waits.
With En Prison, the eligible stake stays on the table after zero. If the next result is a winning non-zero number for that bet, you recover the original stake without profit. A losing non-zero number takes it. What happens if zero repeats depends on the table’s rules; check those before choosing where to play.
You can now read a chip’s position, follow a round and separate a payout from a profit. The next question is the table itself: how many zeros does it have, and which rules does it use?
11 · THE ROULETTE FAMILY
Same game. Different odds.
Before you choose a number, look for the zeros. One small detail changes every bet that follows.
Four names. Three pocket counts.
One zero. Standard payouts. The reference point for the comparisons that follow.
- Chance of red
- 48.65%
- Edge on red
- 2.70%
- Edge on a straight bet
- 2.70%
Count the pockets, not the name.
European roulette has 37 pockets: the numbers 1 to 36 and a single zero. American roulette adds 00, making 38. Triple-zero roulette adds a third green result, making 39. The ordinary payout for a single number stays 35 to 1 across all three. More possible results, the same reward: that is the difference you are buying into.
French roulette usually uses the same single-zero wheel as European roulette. The useful question is which rules the table offers. With La Partage, zero returns half of a red/black, odd/even or low/high stake. A bet on an individual number gets no such protection. The comparison here uses French roulette with La Partage; the name alone is not a promise of that rule.
A green pocket is still a number you can bet on. What makes it special is that it belongs to neither red nor black, neither odd nor even, and neither 1–18 nor 19–36. It adds a way for all of those bets to lose.
12 · THE POWER OF ZERO
Zero is not nothing.
Eighteen red. Eighteen black. It looks like a fifty-fifty choice — until the wheel makes room for green.
The missing unit.
Imagine staking 1 unit on red on a single-zero wheel. There are 18 results that give you 1 unit of profit and 19 that lose your unit. Add those possibilities together: +18 minus 19 leaves −1. Divide by the 37 equally likely outcomes and the average loss is 1/37 of the stake, or about 2.70%.
This is an accounting of possible outcomes, not a prediction that the next 37 spins will contain each number once. Real results can repeat, cluster and leave some numbers unseen for a long time.
Red bet · standard single zero. The red slice is the expected loss, not a fee taken from every bet.
What does 97.30% RTP actually mean?
RTP means return to player: the theoretical share of total stakes returned over a very large number of bets, including returned winning stakes. House edge is the share lost on average. For an ordinary single-zero bet, they are about 97.30% and 2.70%, which add up to 100%.
Total staked is not the same as money brought to the table. If you stake 10 units on each of 100 spins, you have wagered 1,000 units, even if some of those units were winnings you used again. The mathematical expected loss is about 27.03 units. Your actual session can finish far above or below that figure.
13 · ODDS, BETS & PAYOUTS
A payout is only half the story.
Thirty-five to one sounds generous. To judge it, you need the other number: how many ways can this bet lose?
Profit is not the whole return.
A winning 10-unit straight bet pays 350 units of profit and gives back your 10-unit stake: 360 units returned. On a single-zero wheel, though, that number has only one chance in 37. A mathematically fair payout would be 36 to 1 in profit. The actual 35 to 1 leaves the same 2.70% edge as an ordinary bet on red.
Covering more numbers makes wins more frequent and smaller. It does not improve the average return on an ordinary European table. Change the bet below and watch the winning share and reward move together.
- Profit when it wins 1 to 1
- +10
- Total returned when it wins Profit + original stake
- 20
- House edge / theoretical RTP
- 2.70% / 97.30%
- Total staked 10 × 100 rounds
- 1,000
- Expected loss Average over many repetitions; not a session prediction
- 27.03
All amounts are in units. Ordinary payouts; no bonus or multiplier rules.
One American bet breaks the pattern.
The American five-number basket covers 0, 00, 1, 2 and 3 and pays 6 to 1. Five winning outcomes return seven times the stake, including the stake itself: 35 units for every 38 units in the outcome ledger. That means a 7.89% house edge, worse than the ordinary American edge of 5.26%. A larger group is not automatically a better deal.
These calculations use conventional payouts and equally likely, independent results. Multiplier games, bonus bets and promotional rules need their own calculations. Check the actual table rules before applying a percentage.
14 · CAN YOU BEAT ROULETTE?
Can a system change the odds?
Double after a loss. Follow a hot number. Wait for black to be due. The ideas sound different; each asks the past to help with the next spin.
A small win can hide a large risk.
Martingale doubles the stake after every loss. Starting with 1 unit, six losses cost 1 + 2 + 4 + 8 + 16 + 32 = 63 units. The next bet is 64. If that one wins, the whole sequence makes just 1 unit of profit. If the table maximum is 32, you cannot place it at all.
Fibonacci and D’Alembert increase bets more gradually. They change the pattern of wins, losses and required funds, but an ordinary bet still has the same negative expectation per unit staked. A system can produce winning sessions without producing a mathematical advantage.
The experiment
Thousands of sessions.
No chosen winners.
Same wheel. Same starting funds.
Six different ways to bet.
Choose the conditions and run a fresh experiment. No real money is used.
One base stake on red every spin. No change after a win or a loss.
How many small wins can one losing run erase?
Run the experiment to reveal all six systems.Mean = total net result divided by all sessions. Median = the middle result after sorting. A positive net is profit; a negative net is loss.
First 24 sessions · green finishes at or above the starting funds; coral finishes below. A short line is a stopped session.
Where every session finished
Final net results · bars count sessions in equal-width intervals. The full range, including outliers, is shown.
| System | Mean net | Median net | Finished ahead | Funds stop | Limit stop | Mean staked | Expected loss* |
|---|
*Average total staked × house edge. It is a mathematical benchmark, not the measured mean. “Funds stop” means the next required stake was unaffordable, even if some funds remained. If both limits fail, it counts as a funds stop. The experiment uses standard zero losses, without La Partage.
How the six systems bet
- Flat betting
- One base stake on red every spin. No change after a win or a loss.
- Martingale
- Bet on red. Double after a loss; return to the base stake after a win. A run of losses grows the next bet very quickly.
- Fibonacci
- Bet on red using 1, 1, 2, 3, 5, 8… times the base stake. Move one place forward after a loss and two back after a win, stopping at the start.
- D’Alembert
- Bet on red. Add one base unit after a loss; subtract one after a win, with a minimum of one.
- Hot number
- Stake the base amount on the most frequent result in the previous 12 spins. Ties use the lowest result, with 00 after 36.
- Cold number
- Stake the base amount on the least frequent result in the previous 12 spins. Ties use the lowest result, with 00 after 36.
Give every system the same spins.
The experiment compares six precisely defined approaches. Within each simulated session they see the same sequence of fair, independent outcomes. Each starts with the same funds. A session stops before the next prescribed bet would exceed those funds or the table maximum; the simulation never lends extra money or quietly reduces the stake.
Hot and cold approaches look only at the previous 12 results, after 12 unbet opening spins. Every session, including those that stop early, stays in the results. The lines show the first 24 sessions, not the best 24. Run it again and you will get a fresh sample.
Ten reds behind you. Still 18 black pockets ahead.
The wheel has no memory.
On a fair single-zero wheel, black has 18 chances out of 37 on the next spin. That remains true after five reds, ten reds or no red at all. A streak can be surprising when viewed from its beginning; once it has happened, it does not make black due.
The lesson is not that every player loses every session. Some finish ahead. It is that changing stakes or consulting past numbers does not remove the edge under these rules. Total action matters: a system that repeatedly puts more money at risk also exposes more money to that edge.