Roulette (named after the French word meaning "little wheel") is a casino game that emerged from the Italian game Biribi. Players at the roulette table can engage in a variety of betting strategies, placing their chips on individual numbers, clusters of numbers, colors such as red or black, or bet on whether the outcome will be odd or even, or high (19-36) or low (1-18). The thrill of watching the wheel spin and the ball bounce around its edge makes this game an all-time favorite among casino enthusiasts.

To determine the winning number, the croupier spins the roulette wheel in one direction and simultaneously launches the ball in the opposite direction along a tilted track that encircles the wheel. As the ball gradually loses momentum, it traverses a series of deflectors and ultimately settles into one of the numbered pockets on the wheel. This exciting moment culminates in the announcement of the winning number, where successful bets are paid out according to the odds associated with the specific wager.

The origins of roulette date back to 18th-century France, with many historians attributing its invention to mathematician Blaise Pascal in his quest for a perpetual motion device. This revolutionary game evolved from a hybrid of earlier gaming wheels and the Italian game Biribi. The first iterations of roulette featured a simplistic design, with numbers 1 to 28, a single zero, and a double zero. Among these, the seeked thrill of winning was palpable, leading to its rapid popularization across Europe and beyond.

Roulette first gained notable exposure in its modern form in Paris around 1796, where one can find references in literature, including Jaques Lablee's French novel that depicted the layout of a roulette table featuring two slots reserved for the bank. This detail illustrates how the house maintains its mathematical advantage, with the house pockets being a critical component of the game mechanics.

In 1843, the introduction of the single zero wheel at the Bad Homburg casino by François and Louis Blanc marked a significant turning point in the roulette landscape, directly competing with traditional double zero setups. This change significantly improved the odds for the player, making the game increasingly appealing and facilitating its spread across European casinos, particularly in Monte Carlo where it became a staple of the elite gambling scene.

Contrastingly, in early American roulette, the introduction of an American Eagle pocket alongside the existing numbers created an additional edge for the house. This unique layout, albeit short-lived, paved the way for the standardization of roulette in the United States, leading to the familiar double zero wheel that persists today. On the other hand, single zero wheels remain prevalent in most global markets.

The late 19th century saw roulette gain immense popularity across Europe and the United States. The Blanc family's move to Monte Carlo presented a pivotal moment in the history of the game, establishing a premium gambling destination where roulette flourished with the single zero wheel variant. Meanwhile, the American adaptation of roulette remained rooted in the double zero structure, leading to significant disparities in gameplay and house advantage.

As roulette spread throughout the American frontier, casinos faced challenges with rampant cheating, prompting changes in design that elevated the wheel above table level to thwart dishonest tactics. Over time, the American roulette style evolved amidst a backdrop of hasty gambling operations, contrasting with the sophisticated ambiance of European casinos that emphasized leisure and style. This divergence in cultural approaches to gambling became emblematic of the broader gambling experience on either side of the Atlantic.

In the 20th century, iconic destinations for gambling, such as Monte Carlo, maintained their status as premier locations featuring traditional European roulette, while Las Vegas showcased the American double zero wheel as a centerpiece of its glitzy casinos. The proliferation of casinos in the latter half of the century facilitated the global reach of roulette, leading to its establishment as a preferred game in gambling establishments worldwide.

Roulette players enjoy a rich array of betting options that heighten the excitement of each spin. Inside bets offer the chance to wager on specific numbers, while outside bets allow players to wager on broader groupings defined by characteristics like color or parity, enhancing the strategic element of the game. The payout odds are meticulously calculated based on each bet's probability, ensuring a fair and engaging gambling experience for all participants.

Typically, each roulette table has established minimum and maximum betting limits, creating a structured environment for both novice and experienced players. Certain casinos may utilize distinct colored chips to differentiate between players’ inside bets, facilitating smoother gameplay. The thrill of waiting for the ball to settle into a pocket continues until the dealer announces, "no more bets" or the French phrase "rien ne va plus" to signal the end of the betting period.

Once the winning number is established, the dealer places a marker, often referred to as a dolly, on that number’s space on the layout. This action signifies the conclusion of the betting period, prohibiting further wagers or adjustments. The dealer then clears away all losing bets while simultaneously determining payouts for the winning bets placed on the inside and outside options. Once payouts are completed, the dolly is lifted, allowing players to collect their winnings and prepare for another round. Winning chips remain on the table until claimed by the player.

Roulette players have multiple avenues for placing their bets. Inside bets allow participants to target a singular winning number or a small cluster of adjacent numbers, while outside bets encompass broader categories based on attributes such as color or parity (odd/even). Each bet option comes with distinct payout odds, which directly correlate with their respective probabilities of occurrence.

The rules governing the roulette table stipulate both minimum and maximum betting limits, often enforcing these limits for all of a player’s inside and outside bets during each spin. In some establishments, unique roulette chips in various colors are employed to help distinguish the bets made by different players. Enthusiasts are permitted to place wagers as the ball continues its journey around the wheel until the dealer pronounces "no more bets" or the French term "rien ne va plus".

When the dealer identifies the winning number and color via the roulette wheel's outcome, they will place a dolly marker on that specific number on the layout. This action signals that no players can place any more bets, collect, or remove any existing bets. The dealer will then sweep away all losing bets using their rake or by hand and proceed to determine payouts for any winning inside or outside bets still active on the layout. Following the completion of the payout process, the dolly is removed, allowing players to reclaim their winnings and place new bets for the next round.

In 2004, California sanctioned a unique variant of roulette dubbed California Roulette. This variation mandates the use of playing cards instead of the traditional slots on the roulette wheel to determine the winning number. Such adaptations showcase the ongoing evolution and innovation within the world of casino gaming, catering to a diverse set of player preferences and regulatory frameworks.

The pockets of the roulette wheel are meticulously numbered from 0 to 36.

In ranges from 1 to 10 and 19 to 28, odd numbers are designated red and even numbers black. Meanwhile, in ranges from 11 to 18 and 29 to 36, odd numbers are black and even numbers red.

Additionally, there exists a green pocket numbered 0 (zero), and in American roulette, there is a second green slot marked 00. The arrangement of the pockets on the roulette wheel adheres to a defined clockwise sequence across most casinos:

Single-zero wheel

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

Double-zero wheel

0-28-9-26-30-11-7-20-32-17-5-22-34-15-3-24-36-13-1-00-27-10-25-29-12-8-19-31-18-6-21-33-16-4-23-35-14-2

Triple-zero wheel

0-000-00-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-18-29-7-28-12-35-3-26

The betting area on a roulette table is known as the layout. The layout can either be single-zero or double-zero in style.

The European layout features a single zero, while the American layout typically incorporates a double zero. The American roulette tables are now commonplace in most casinos due to the higher house edge associated with this format, thus appealing to certain player demographics.

On the other hand, the traditional French-style layout, where the wheel is centered with the layout flanking either side, is a rare find outside the glamorous Monte Carlo casinos.

In roulette, players place bets that can be categorized as either inside or outside.

Outside bets generally offer lower payouts but come with a higher probability of winning. However, all outside bets result in a loss should a zero appear on the wheel.

1 to 18 (low or manque), or 19 to 36 (high or passe)

A bet that the winning number will fall within the selected range.

Red or black (rouge ou noir)

A wager predicting that the winning number will be of the chosen color.

Even or odd (pair ou impair)

A bet that the winning number will exhibit the chosen parity. Unlike in mathematical terms, 0 is neither even nor odd.

Dozen bet

A wager predicting that the winning number will fall into one of three selected dozens: first (1-12, Première douzaine), second (13-24, Moyenne douzaine), or third (25-36, Dernière douzaine).

Column bet

A wager predicting that the winning number will come from one of the chosen vertical columns of 12 numbers on the table, such as 1-4-7-10 down to 34.

Snake bet

A special wager covering the numbers in a snakelike pattern: 1, 5, 9, 12, 14, 16, 19, 23, 27, 30, 32, and 34, which shares the same payout structure as dozen bets.

In selected casinos, the outermost bets (low/high, red/black, even/odd) are subject to a unique feature known as the "halfback" or la partage rule, which allows players to reclaim half their bet should a zero land. Alternatively, some establishments employ the "imprisonment" or en prison rule, wherein a loss on outside bets results in the players' stakes being held until the next spin—if that spin results in a win, the initial wager is refunded.

The expected value of a standard $1 bet can be calculated for both American and European roulette:

{\displaystyle {\text{expected value}}={\frac {1}{n}}(36-n)={\frac {36}{n}}-1,}

Where n is the total number of pockets within the wheel. The initial bet is always returned in conjunction with the indicated payout, demonstrating that this payout formula leads to a zero expected value of profit when only 36 numbers are present, giving the casino a necessary edge through the inclusion of additional pockets.

Bet name	Winning spaces	Payout	French		American
			Odds against winning	Expected value (on $1 bet)	Odds against winning	Expected value (on $1 bet)
0	0	35 to 1	36 to 1	−$0.027	37 to 1	−$0.053
00	00	35 to 1			37 to 1	−$0.053
Straight up	Any single number	35 to 1	36 to 1	−$0.027	37 to 1	−$0.053
Row	0, 00	17 to 1			18 to 1	−$0.053
Split	Any two adjoining numbers vertical or horizontal	17 to 1	17+1⁄2 to 1	−$0.027	18 to 1	−$0.053
Street	Any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.)	11 to 1	11+1⁄3 to 1	−$0.027	11+2⁄3 to 1	−$0.053
Corner	Any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21, etc.)	8 to 1	8+1⁄4 to 1	−$0.027	8+1⁄2 to 1	−$0.053
Top line (US)	0, 00, 1, 2, 3	6 to 1			6+3⁄5 to 1	−$0.079
Top line (European)	0, 1, 2, 3	8 to 1	8+1⁄4 to 1	−$0.027
Double street	Any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.)	5 to 1	5+1⁄6 to 1	−$0.027	5+1⁄3 to 1	−$0.053
1st column	1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34	2 to 1	2+1⁄12 to 1	−$0.027	2+1⁄6 to