• Roulette Odds And Payouts
• Roulette Odds Red Or Black
• Vegas Roulette Odds
• Roulette Odds Of Hitting Red 10 Times
• Best Roulette Odds

By Ion Saliu, Founder of Roulette Mathematics

This question was posted in mathematical newsgroups (alt.math.recreational, alt.math.undergrad, alt.sci.math.probability): 'Winning and Quitting on Red/Black in Roulette'.

A European Roulette table has one zero (green), 18 red and 18 black slots. In total there are 37 slots for the roulette ball to land on. The odds that the Roulette ball will land on red is 18/37 = 48.6%. The odds that the ball will land on red two times in a row is 48.6% x 48.6% = 23.6%.

• For example, the probability of losing if you bet on red is 19/37 (18 black numbers + 1 green number). Note: To reduce a fraction down to 1/X, just divide each side by the number on the left. A bet on red has the probability of 18/37, divide each side by 18 and you've got 1/2.05.
• Roulette Odds Calculator. Many websites offer roulette odds calculators online for giving players an estimate of what the results of their bet will be. Roulette is a game of chance, but the odds of a roulette table can be calculated with statistics. The calculators work assuming a player uses the same betting number throughout the game.
• Record Repetition of the Same Color in Roulette. There are no exceptions that the same color appeared more than 20 times in a row in practice. The record was registered in 1943, when red color came up 32 times in a row! The probability of such event in French Roulette is (18/37) 32 = 0.96886885 with the corresponding odds.

'Obviously in roulette betting on in the long run you are going to lose your money but at some point chances are you'll be in profit. To take an extreme example if you had $1000 you could reasonably expect to be up $1 at some point. Is it possible to generalize this? I want to win W dollars at which point I will quit. How much cash C would I need to have probability P of succeeding? Let's say I'm betting on a 37 number roulette wheel (18 red 18 black and one green 0)?'

On the surface, the best probability for the roulette player to be ahead is in one trial (spin): 48.6% to win (versus 51.4% to lose), as far as even-money betting is concerned. I don't agree that it is the best strategy (betting all your bankroll on one spin).

Theoretically, no bankroll will put a player ahead guaranteed, IF flat-betting and playing very long consecutive sessions. There are moments, however, when the roulette player can be ahead by at least one betting unit. Even in even-money bets, the player has a good chance to be ahead by at least one unit after 5, or 10, or even 100 spins. But more than 20 spins are NOT recommended; the probability (odds) to lose go(es) above 50%! Think about it!

The main thing, mathematically, is the number of player's wins in N trials. To be ahead, means the player has won at least one more roulette spin (number of successes) than the number of losses in N trials. The question then becomes:

'What are the probabilities for the player to be ahead in various numbers of trials?'

Everybody can use my probability software SuperFormula, option L: At Least M successes in N trials.
Winning probability: p = 18/37; M must be at least (N/2) + 1.
Here is a number of cases from the player's perspective.

The figures are applicable to all even-money roulette bets: black or red; even or odd; low or high (1-18 or 19-36).

1 trial (spin)
- probability (odds) to win: 48.6%; odds = 1 in 2.05
- probability (odds) to lose: 51.4%; odds = 1 in 1.95
(the probability to lose is 19/37; adding zero to unfavorable cases).

2 trials (spins)
- probability (odds) to win 2 of 2: 23.7% (1 of 2 doesn't mean 'being ahead')
- probability (odds) to lose 1 of 2: 76.3%

3 spins
- probability (odds) to win at least 2 of 3: 48%
- probability (odds) to lose at least 2 of 3: 52%

10 spins
- probability (odds) to win at least 6 of 10: 34.4%; odds = 1 in 2.91
- probability (odds) to lose at least 6 of 10: 41.1%; odds = 1 in 2.43

20 spins
- probability (odds) to win at least 11 of 20: 36.5%
- probability (odds) to lose at least 11 of 20: 46.2%

100 spins
- probability (odds) to win at least 51 of 100: 35.5%; odds = 1 in 2.82
- probability (odds) to lose at least 51 of 100: 56.8%; odds = 1 in 1.76.
It's getting worse for the player...

The roulette strategy (or system) is a totally different ball game! But there are professional gamblers out there, including roulette players! They must have strategies, some roulette systems deduced from some figures like the ones above! The player can be ahead at any point in the game. If so, maybe it's time to move to another (or casino) table: It improves the odds of winning!

Always keep track of the losing and winning streaks. Be strong and put an end to a winning streak. You are ahead, you quit the roulette table. Go to another table and wait until you are ahead. The bankroll is of the essence: It must assure going through long losing streaks. Divide the streaks in 10 spins or 20 spins. Never fight aggressively short or mid-term losing streaks. This is the best approach for those who do not know Ion Saliu's casino gambling systems. A good approach to gambling is the next best thing to a good gambling system! Applicable to blackjack and baccarat, too!

Axiomatic one, everybody knows that the casinos have an edge or house advantage (HA) in all the games they offer, roulette including. The house advantage is created by the payouts in rapport to total possibilities for the respective bet. We can apply this simple formula based on units paid UP over total possibilities TP:

HA = 1 – (UP / TP)
(always expressed as a percentage.)

For example, in single-zero roulette, the one-number (straight-up) bet has payout of 35 to 1. The to qualifier is very important: the casino pays you 35 units and they give you back the unit you bet; thus, you get 36 units. There are 37 possibilities in single-zero roulette: 36 numbers from 1 to 36 plus the 0 number. Therefore, HA = 1 – (UP / TP) = 1 – (36 / 37) = 1 – 0.973 = 0.027 = 2.7%.

Let's calculate HA for the 1 to 1 bets: black/red, even/odd, low/high. HA = 1 – (UP / TP) = 1 – (2 / 2.055) = 1 – 0.973 = 0.027 = 2.7%. There are little differences among bets depending on how many decimal points we work with in our calculations.

The point is, the casinos have an advantage, or the players have a disadvantage. Nonetheless, the players' disadvantage is far better than what they face in state-run lotteries. Yet, most casino gamblers lose big, including at roulette tables. They do not have sufficient bankrolls to withstand long losing streaks.

However, around 45% of the roulette numbers lead the gamblers to profits in a few thousand spins. That is, with a sufficient bankroll, a player has a pretty good chance to make a profit, even if playing a random roulette number, or a favorite number. I analyzed about 8000 roulette spins from Hamburg Spielbank (casino). Quite a few numbers ended up making a profit: roulette systems, magic numbers.

By contrast, the more lottery drawings a player plays, the higher the degree of certainty of a loss. Let's make a comparative analysis to the roulette long series above (spins: total roulette numbers, 37, multiplied by 200). If playing the pick-3 lottery for some 100,000 drawings, it is guaranteed that all pick-3 straight sets will be losers. Some numbers will hit up to 3% to 5% above the norm — but that is not nearly enough to assure a profit. A frequency of 3% to 5% above the norm leads to profits in roulette, however.

Ion Saliu's Paradox and Roulette

Ion Saliu's Paradox of N Trials is presented in detail at saliu.com, especially the probability theory page and the mathematics of gambling formula. If p = 1 / N, we can discover an interesting relation between the degree of certainty DC and the number of trials N. The degree of certainty has a limit, when N tends to infinity. That limit is 1 — 1/e, or approximately 0.632....

If you play 1 roulette number for the next 38 spins, common belief was that you expected to win once. Not! Non! Only if you play 38 numbers in 1 spin, your chance to hit the winning number is 100%. Here is an interesting table, which includes also The Free Roulette System #1 presented at the main roulette site.

The maximum gain comes when playing 38 numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as Free System #1 scares most gamblers. 'Play 34 or 33 numbers in one shot? I'll have a heart attack!' In reality, the Free Roulette System #1 offers a 28.8% advantage over playing singular numbers in long sessions. That's mathematics, and there is no heart to worry about, axiomatic one.

You can also use SuperFormula to calculate all kinds of probabilities and advantage percentages. The option L — At least M successes in N trials is a very useful gambling instrument. If you play 19 numbers in one spin, the probability to win is 50%. If you play 19 numbers in 2 consecutive spins, the probability to win at least once is 75%.

Editor's note
• In an apparent change of heart, the Hamburg casino (Spielbank) offers online roulette results for free. The new link is (for the time being!):

www.spielbank-hamburg.de/spielsaal/permanenzen.php4

• • Real-life roulette spins are also available from the Wiesbaden, Germany, Casino (Spielbank)

www.spielbank-wiesbaden.de/DE/621/Permanenzen2.php: Wiesbaden Spielbank Permanenzen

Roulette: Software, Systems, Super Strategy

See a comprehensive directory of the pages and materials on the subject of roulette, software, systems, and the Super Strategy.

• Theory, Mathematics of Roulette Systems, Strategies, Software.
• The Best-Ever Roulette Strategy, Systems based on mathematics of progressions and free-for-all.
• An inventory of free and outrageously pricedroulette systems.
• Software, Systems: Roulette Wheel Positioning, Sectors, Birthday Paradox.
• 'Roulette System that Won Millions!'
  ~ Ion Saliu's roulette theory, systems, and software were pirated by an Australian gambling group.
• James Bond Roulette System for Dozens, Columns.
• Roulette Systems, Threats from Casino Chairman.
• Anti-Gambler Advice from John Patrick, Casino Moleextraordinaire and conspirator.
• Wizard of Odds Had High Praise For Ion Saliu's Gambling Theory.
• Casinos pay troubled individuals to intimidate intelligent gambling system authors.
• Download roulette, blackjack, casino gambling, systems, software.

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KNOW YOUR ROULETTE ODDS

Roulette odds provide you with the information you need to know how likely you are to win any bet. There are many different bets available on a roulette table, and each one has its own odds. These range from even money bets that pay off nearly half the time, to single number bets that are hard to hit, but which will earn you a lot of money when they do.

Before diving deeper into roulette odds, however, it’s important that you understand the basics of how to play roulette. Before every spin, you will have the opportunity to place as many bets as you like all around the roulette table. Each of these bets covers one or more of the numbered pockets on the roulette wheel, and comes with its own specific odds of winning.

When the croupier spins the ball around the wheel, it will eventually fall into one of these pockets. The number and color of that pocket will determine which bets win on that spin. At this point, the croupier will mark the winning number, losing bets are taken off the table, and roulette payouts are made for the remaining winning bets before the next spin.

AMERICAN VS. EUROPEAN ROULETTE PROBABILITIES

While the American and European games may seem similar at first glance, the two games actually use different roulette wheels. The American wheel has both a zero (0) and a double zero (00) on it, while the European wheel only has the single zero.

This actually makes a major difference to players. European roulette odds are much better for players, because there is one less pocket on the wheel for the ball to fall into. Since both versions offer the same roulette payouts, this means that the odds and house edge are smaller in European roulette.

Some European roulette games offer additional rules that further help the player cut into the house edge. When a casino offers la partage, that means that you will only lose half of an even money bet (meaning bets like odd/even or red/black) if the ball lands on zero.

En prison is a variation of the la partage rule. Rather than getting half of your bet back, the money will instead be put “in prison”. after which you can win it all back If the next spin results in a win for that bet. In either case, these options offer the best odds in roulette, as they cut the house edge roughly in half.

EUROPEAN	AMERICAN
NO	DOUBLE ZERO	YES
37	NUMBER OF SECTORS	38
2.7%	HOUSE EDGE	5.26%
97.3%	AVERAGE PAYOUT FOR 100 €	94.74%

ROULETTE ODDS AND PAYOUTS EXPLAINED

While there are a wide array of roulette bet types to choose from, these options can mainly be divided into two types: inside bets and outside bets. These categories get their names based on where these bets occur on the roulette table layout. Inside bets are placed on the numbers at the center of the table, while outside bets have special betting areas on the outer portion of the board.

Inside Bets

Inside bets tend to have a lower probability of winning, but they offer the biggest roulette payouts. For this reason, they are often the best way to start playing for those who are new to the game, as they give you a chance to earn a big payout on any given spin without having to risk much money on each bet.

Straight: A bet on a single number. If the ball lands on that number, the bet pays 35-1.

Split: A bet on two adjacent numbers on the roulette table. If either of those numbers hits, the bet pays 17-1.

Street: A bet on a row of three numbers on the roulette layout. If any of those numbers wins, your bet pays out at 11-1 odds.

Corner: A bet on a “square” of four numbers on the roulette betting layout. If any of these numbers wins, the bet pays 8-1.

Six Line: A bet on two consecutive rows, covering six numbers in total. If the ball lands on any of those numbers, you’ll win at 5-1 odds.

First Four: This bet is only available on European roulette tables, and covers the zero along with 1, 2, and 3. If any of those four numbers wins, the bet pays 8-1.

Trio: Like a street bet, this bet covers three numbers, but it includes one of the zeros. For instance, a player can make a trio bet covering 0, 1, and 2. If any of those numbers wins, the bet pays 11-1.

Top Line: This bet is only available on American roulette tables and covers five numbers in total: the zero, double zero, 1, 2, and 3. If the ball lands on any of those numbers, your bet pays out at 6-1 odds.

Outside Bets

Outside bets cover large sections of the wheel, giving you a better chance of winning your bet. However, they also come with smaller payouts, and may require higher minimum wagers than inside bets.

Columns: A column bet covers one of the three columns on the roulette table layout, each of which contains 12 numbers. If any of those 12 numbers wins, your bet pays 2-1 odds.

Dozens: These bets cover sets of 12 consecutive numbers: 1-12, 13-24, or 25-36. If a number in the range you bet on wins, the bet pays 2-1.

Roulette Odds And Payouts

Odd/Even: These bets cover all of the odd or even numbers on the table (note that zeros do not count as either odd or even). If a matching number wins, then your bet pays out even money.

Red/Black: These bets cover all pockets – 18 each – of that color. If the ball lands on that color, you win at even money odds.

High/Low: These bets cover the range of 1-18 and 19-36. Should the ball land on a number in the range you’ve chosen, the bet pays even money.

Called & Announced Bets

Called and announced bets are roulette bet types that may not be familiar even to many experienced players. These are more frequently seen in European casinos, and they allow players to make bets by announcing them to the croupier. Called bets can be made on credit, while announced bets require a player to actually have the money on the table in order to make them.Typically, such bets are only offered to known players, usually high rollers. In modern roulette, announced bets are far more common than called bets, as most casinos cannot or will not allow their players to wager on credit.

While any bet can be an announced bet, this option is typically only used for complex wagers, most of which are known as the French bets. These bets cover specific portions of the roulette wheel, which takes several chips to accomplish and can be unwieldy to manage on the standard roulette betting layout. Instead, the croupier can manage those bets for players, sometimes by using the “racetrack” layout seen on some European roulette tables.

Common announced bets include:Voisins du Zero: This bet covers 17 numbers using nine chips. Your payout will be determined by the type of bet covering the winning number: 16 chips on the corner bet, 22 on the trio, or 17 chips if one of the splits wins.

Jeu Zero: The “zero game” covers just seven numbers using four chips. If a split wins, the bet will pay out 17 chips. If the number 26 hits, you win 35 chips.

Tiers du Cylindre: This bet covers 12 numbers that lie far away from the zero. It takes six split bets to cover these numbers, and you get a payout of 17 chips if any of them wins.

Orphelins: Made with five chips, this bet has varying payouts. The straight bet on 1 pays 35-1, while the split bets would pay 17-1.

Finals: A final bet covers every number that ends in a specific digit. These are all straight bets paying out at 35-1 odds.

Full Completes: A full complete is a true maximum bet on a single number. These bets involve heavy risks to the player, with the exact payouts depending on what number is hit, various table maximums, and which number is being maxed out.

You can find out more details on each of these on our called bets and announced bets page.

THE BEST ROULETTE BETS FOR YOUR BANKROLL

Our team of experts has years of experience playing roulette, meaning we know all the pro tips and tricks that can help you get the best roulette odds possible. One of the most important things we can share is how to make the best bets possible each time you step up to the roulette table. Here are our favorite bets in roulette:

THE WORST ODDS TO WATCH OUT FOR

While we’re happy to give you tips on how to find the best odds in roulette, the best thing we can do for our players is steer them away from bets that aren’t worth their time. By avoiding the worst of the worst options, you’ll improve your roulette odds and have more fun playing knowing you aren’t getting ripped off.

The biggest example is the Top Line or First Five bet on American roulette tables. While the odds in roulette are very consistent across almost all bets, this particular bet is an exception. This is because payouts in roulette are generally designed to be fair for a wheel with 36 pockets, with the house edge coming from the fact that there are actually 37 (European roulette) or 38 (American roulette) pockets for the ball to fall into.

On an American table, that means that whether you make a straight bet at 35-1 payout, or bet on black at even money, the house edge is 2/38, or 5.26%. However, the Top Line bet covers exactly five numbers (0-00-1-2-3), a number that 36 can’t be evenly divided into. Casinos offer 6-1 on this bet, which would only be a fair bet if there were 35 pockets. The result of this is a house edge of 7.89%, which is much higher than on any other bet.

Roulette Odds Red Or Black

The Top Line isn’t always the only sucker bet on the table. Generally, it’s best to avoid unusual side bets that may be added to the game, especially in online roulette. As in other casino games, these side bets are almost always added to make more money off players and come with extraordinarily high house edges.

HOW TO IMPROVE YOUR ODDS AT ROULETTE

One of the best ways to improve your odds in roulette is by brushing up on your roulette strategy. While the results of each spin are random, roulette strategies can be used to manage your sessions and get the kinds of results you’re looking for.

For instance, let’s say you want to maximize your chances of booking at least a small win at the end of a session. Your best bet may be the Martingale System, which asks you to place even money bets, doubling your bet amount after a loss. On the other hand, a player looking for a huge payday would be better off trying something like the Guetting System. We cover many of these systems as well as other ways to improve your odds on our roulette strategy page.

The most important thing you can do to maximize your roulette odds is to get some practice in before you try playing for real money. If you’re looking to develop your skills or test a new betting strategy, you’ll want to check out the 80+ free online roulette titles which are available for you to try without risking any money.

PLAY AT THE TOP ONLINE ROULETTE SITES

At this point, you should have a strong knowledge of roulette odds and payouts, which bets you want to seek out, and which to avoid. Armed with this information, you should feel confident about playing roulette for real cash at one of our top-rated casinos.

We only recommend the most trustworthy and reputable online casinos for our readers. Any of the sites in the table below will provide you with a safe and secure place to enjoy playing roulette.

CASINO	BONUS	RTP	RATING	REVIEW
1	T&C APPLY	PAYOUT	10	READ REVIEW	PLAY NOW
2	T&C APPLY	PAYOUT	9.6	READ REVIEW	PLAY NOW
3	T&C APPLY	PAYOUT	9.3	READ REVIEW	PLAY NOW
4	T&C APPLY	PAYOUT	9	READ REVIEW	PLAY NOW
5	T&C APPLY	PAYOUT	9.4	READ REVIEW	PLAY NOW

FAQ

🎲 Are roulette odds good?

Vegas Roulette Odds

While roulette odds vary depending on the type of table you are playing at, the odds are generally quite good. That’s especially true when compared to other popular gambling options like slot machines, which normally have much higher house edges.

❤️ What is the best bet in roulette?

If you want the best odds in roulette, you’ll want to find a European roulette table where you can take advantage of la partage rules on even money bets. Under those conditions, the house edge is just 1.35%.

🎰 What are the best roulette bet combinations?

There are many different roulette bet combinations that are effective, with the best one depending on your goals at the table. Familiarizing yourself with bet systems can help you determine what works for you, and what doesn’t.

💰 How much is a roulette chip worth?

The most common value for a roulette chip in an American casino is one dollar. However, this amount can vary depending on how much you buy in for at the table. When you purchase your chips, your croupier will set a value that leaves you with a reasonable amount of chips to play with: buy in for $100, and you’ll get dollar chips; start with $10,000 on the table, and each chip might be worth $100 instead.

Roulette Odds Of Hitting Red 10 Times

❓ Are roulette tables rigged?

Generally speaking, roulette tables are fair. Casinos have a mathematical advantage and don’t need to cheat to get roulette odds they are happy with. However, there have been plenty of cases where biased wheels have made some numbers appear more often than others – something that attentive players can take advantage of.

Best Roulette Odds

CASINO	BONUS	RTP	RATING	REVIEW
1	T&C APPLY	PAYOUT	10	READ REVIEW	PLAY NOW