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The Labouchère system, also called the cancellation system or split martingale, is a gambling strategy used in roulette. The user of such a strategy decides before playing how much money they want to win, and writes down a list of positive numbers that sum to the predetermined amount. With each bet, the player stakes an amount equal to the sum of the first and last numbers on the list. If only one number remains, that number is the amount of the stake. If the bet is successful, the two amounts are removed from the list. If the bet is unsuccessful, the amount lost is appended to the end of the list. This process continues until either the list is completely crossed out, at which point the desired amount of money has been won, or until the player runs out of money to wager.^[1]

Description of the gameplay[edit]

The theory behind this Labouchère system is that, because the player is crossing two numbers off of the list (win) for every number added (loss) the player can complete the list, (crossing out all numbers) thereby winning the desired amount even though the player does not need to win as much as expected for this to occur.

It should be mentioned that the Labouchère System is meant to be applied to even money Roulette propositions such as Even/Odd, Red/Black or 1–18/19–36. When any of these bets are made in the game of Roulette, a spin resulting in a '0' or '00' results in a loss, so even though the payout is even money, the odds are clearly not 50/50. The Labouchère System attempts to offset these odds.

If a player were to play any one of the above propositions, there are eighteen individual results which result in a win for that player and (for an American Roulette wheel) twenty individual results that result in a loss for that player. The player has an 18/38 chance of success betting any of the above propositions, which is around 47.37%.

Theoretically, because the player is cancelling out two numbers on the list for every win and adding only one number for every loss, the player needs to have his proposition come at least 33.34% to eventually complete the list. For example, if the list starts with seven numbers and the player wins five times and loses three (62.5% winning percentage) the list is completed and the player wins the desired amount, if the list starts with seven numbers and the player wins 43,600 times and loses 87,193 times (33.34% winning percentage) the list completes and the player wins.

A formula to understand this is as follows:

When

The result is the list being completed.

Assuming a player bets nothing but black (red/black proposition) and black can be expected to hit 47.37% of the time, but the system only requires that it hit 33.34% of the time, it can be said that black only need hit approximately 70.38% of the time (33.34/47.37) it can generally be expected to in order for the system to prevail.

An obvious downfall to the system is bankroll, because the more losses sustained by the player, the greater the amount being bet on each turn (as well as the greater the amount lost overall) is. Consider the following list:

10102020201010

If a player were to bet black and lose four times in a row, the amounts bet would be: $20, $30, $40, and $50. By taking these four consecutive losses, the player has already lost $140 and is betting $60 more on the next bet. Consecutive losses, or an inordinate number of losses to wins can also cause table limits to come into play.

Occasionally, a player following this system will come to a point where he can no longer make the next bet as demanded by the system due to table limits. One work-around for this problem is simply to move to a higher limit table, or a player can take the next number that should be bet, divide it by two and simply add it to the list twice. The problem with the latter option is that every time a player commits such a play, it will infinitesimally increase the percentage of spins a player must win to complete the system. The reason this is so is because the player is adding two numbers (which both will be crossed out in the event of wins) where only one loss was sustained.

To prove this, if a player were to play the Labouchère system the same way with the exception being that the player always added half of the wager lost to the bottom of the list twice for every wager lost where:

When:

The result is the list being completed.

The player would actually have to win in excess of 50% of the time (the actual percentage of wins necessary, given x and y, being dependent on z) in order to complete the list, or more than the player could actually be expected to win.

Algorithm[edit]

The algorithm for the Labouchère system can be considered a Las Vegas algorithm since the amount of money a player desires to win will always be a predetermined amount. However, there is no guarantee that the player will reach the desired goal before the bankroll is lost. This is referred to as risk of ruin. For instance, consider the recursive implementation of a round of Labouchère betting in Python.

The recursion of the algorithm terminates when the sequence is empty or when the player possesses insufficient funds to continue betting. When the function is called, the size of the bet made is equal to the sum of the first and last numbers of the sequence. If the length of the sequence is one, then the bet is equal to the sole member of the sequence. If the bet is won, then the first and last members are spliced from the sequence and the next round begins. However, if the bet results in a loss, then an integer equal the size of the lost bet is appended to the sequence and the next round begins. As determined by the parameters for termination of recursion, the only cases in which the algorithm will terminate are those in which the player has either won an amount equal to the summation of the original sequence or has lost all of their available capital. ^[2]

Reverse Labouchère[edit]

The Labouchère system can also be played as a positive progression betting system; this is known as playing the reverse Labouchère. In this version after a win, instead of deleting numbers from the line, the player adds the previous bet amount to the end of the line. You continue building up your Labouchère line until you hit the table maximum. After a loss, the player deletes the outside numbers and continues working on the shorter line. The player starts their line again if they run out of numbers to bet.

The Reverse Labouchère system is often used because where the Labouchère list represents how much the player wants to win, a reverse Labouchère line represents the most that the player will lose during the betting cycle. It is with this that a player with a bankroll of x can create their own line, or lines, representative of the maximum amount that they can sustain in losses.

Additionally, a player does not necessarily have to continue the system until the table limit is met or exceeded, but could instead pick a single bet that the player does not wish to exceed and make that bet their own personal limit.

Unlike the Labouchère system which (when adhered to strictly) requires a winning percentage of at least 33.34% to complete, the winning percentage needed to complete a Reverse Labouchère line is going to be dependent on both the table limit (or the maximum single bet a player is willing to make) as well as the numbers on the initial line in relation to the table limit.

For example, if a table had a limit of $500 and a player composed a Reverse Labouchère line as follows:

50, 50, 50, 50, 50

Nine consecutive wins (100, 150, 200, 250, 300, 350, 400, 450, 500) would cause the next bet in the system to exceed the table limit, and thus the line would be completed with a player profit of $2,700.

In contrast, if a player composed a Reverse Labouchère line such as:

25, 25, 25, 25, 25

Nineteen consecutive wins (50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500) would cause the next bet in the system to exceed the table limit, thus the line would be completed with a player profit of $5,225.

The length of the line in the Reverse Labouchère system is also important as it relates to the percentage of wins necessary to complete the system. For example, if a line of:

50, 50, 50, 50, 50

suffers three consecutive losses as soon as the system begins, then the line is completed and a new line must be started, or the player may choose to quit.

In contrast, if a line of:

50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50

suffers three consecutive losses, then there are still six numbers remaining on the list. In the line immediately above, it would take an opening streak of six consecutive losses for the line to be completed.

All other things remaining the same, the longer a player's line, the more the player is risking losing. However, the longer the player's line, the better winning percentage the casino need have in order to break the player's line.

Advocates of this system point out that when a player uses the Labouchère System, where a streak in the casino's favor, or many mini-streaks in the casino's favor, will cause the player to sustain a huge loss, a single streak, or a few streaks in the player's favor using the Reverse Labouchère system will cause the player to have a huge gain.

A formula that can be used to determine how this system could fail is as follows:

Where:

When:

The system has failed, and all numbers on the line are crossed completely out.

Given an infinite line, the Labouchère System when played by the player requires a winning percentage of at least 33.34% to complete. In contrast, for the Reverse Labouchère to fail requires only that the player lose 33.34% of the time.

Once again, the winning percentage necessary for the system completing to success depends upon a number of variables.

References[edit]

1. ^Burrell, Brian. Merriam-Webster's Guide to Everyday Math. Merriam-Webster.
2. ^Billings, Jake; Del Barco, Sebastian (2017). 'An Investigation into Labouchère's Betting System to Improve Odds of Favorable Outcomes to Generate a Positive Externality Empirically'. arXiv:1707.00529 [q-fin.GN].

• Tijms, Henk (2004). 'Probabilities in everyday life'. Understanding probability: chance rules in everyday life. Cambridge University Press. pp. 91–93. ISBN0-521-54036-4.

There are three primary ways to play roulette online, depending on your goal in playing and what state you live in.

Roulette is a popular casino game that means “little wheel” in French. It draws many players because it’s one of the most accessible table games to understand and play. Anyone who happens to be interested in a slow-paced table game that can be picked up in minutes will find that roulette is a great option. If you’re interested in learning more about free roulette at legal online casinos, read on for all the information you could need.

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Playing Free Roulette At Legal Online Casinos

Since roulette is easy to play for beginners, it’s a popular option at both land-based and legal online casinos. If you’ve enjoyed playing it in the past at a physical location, it’s easier than ever to play a few games for free from the privacy of your own home.

Do Legal Online Casinos Offer Roulette Games?

Many of the legal online casinos in states like New Jersey and Pennsylvania do offer roulette games that you can play. While many of these games will be paid, there may also be demos or practice modes where you can play roulette for no fee whatsoever. This is a great way to try this game or get some practice with a strategy so you can increase your number of wins.

It’s essential to choose reputable online roulette providers, which can be done by looking for online legal providers and see which of them offer a free version of their games. While there are other sources of free roulette, not all websites can be trusted. Make sure you know who is running the site and that it is a legitimate casino.

Do I Need An Account To Play Free Roulette Games Online?

It depends on where you decide to play free roulette games. There are many sites where you can hop on, play a few games, and leave without ever making an account. This is a convenient option for someone who wants to get into the game without having to do any extra work.

However, other sites do require you to register before playing. There is often some kind of reward for doing so, which makes it worth making an effort. Signing up at real-money casino websites is also an option if the provider offers free games in addition to the paid ones. If you take a look at the various options, you’ll likely find one that fits your preferences.

Is There Any Way To Win Real Money Playing Free Roulette?

There aren’t a ton of options for making real money by playing free games, but it is a possibility. However, keep in mind that most legal casinos with free games only offer points or fake currency. The main exception to this is a sweepstakes site, where you can collect various forms of coins, and some of them can be turned into real money that you can deposit into your bank account.

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Playing Roulette For Real Money Online

While free versions of roulette are available online, there are also options to play for real money on the Internet. This is determined by state so not everyone can access these options. However, more and more states are adding legalized online gambling every year, with Michigan expecting to launch in the months to come.

States With Legal Online Roulette

When it comes to legal online roulette, you can find real money games in the following states:

• Delaware

Since all of these states allow online casinos, that also means that roulette can be provided in those locations. Many of these states have slot games, as well as table games like roulette, blackjack, baccarat, and craps. However, you will need to check individual casinos to determine whether they offer roulette as part of their online selection of games.

How Many Different Roulette Games Are Available?

While the main types of roulette are single zero, double zero, and triple zero, that doesn’t mean that these casinos only offer three games. Many of them will have several rooms and may even incorporate different themes for each of them so players can find a game that appeals to their interests.

Some of these casinos might have a single type of roulette in a few different rooms, while others offer dozens of choices. For instance, Tropicana Casino has rooms designated as American roulette and European roulette, as well as having rooms for single zero and double zero roulette. Double zero roulette is the same thing as American roulette, but this allows everyone to find the roulette they are most comfortable with.

What Are The Smallest Stakes You Can Play Online?

If you’re interested in making small bets on roulette, you’re in luck because the game is designed to allow this when you play online. Not only can you often play for just a few dollars (or even cents), but you can also usually take advantage of bonuses for signing up so you can play games for free without making a deposit.

Rather than spending lots of money traveling to a casino, finding lodging, and ordering from expensive restaurants, online casinos also have the perk of not requiring additional funding. With stakes as low as $0.50 at some casinos, you can play with change at home rather than saving up to make a trip to a casino across the state.

Live Dealer Roulette Games At Legal Online Casinos

If you’ve heard anything about online casinos, you might be familiar with the term “live dealer.” Many table games offer both video games where you play only against the house, as well as live dealer games where you are playing with other players and an actual dealer.

What Is Live Dealer Roulette?

Live dealer roulette is a form of roulette where a physical dealer in an actual casino is spinning a roulette wheel for people who are playing online. Also, you will be in a virtual room where other players are also making bets and trying to win. Many people appreciate this kind of setting because you can interact with other players and get a more authentic casino experience with this kind of roulette.

Where Can I Play Live Dealer Roulette For Free Online?

It’s less common to find live dealer games of roulette online, but it still pops up on some sites. The best way to play for free is by visiting an online legal website and using your initial signup bonus to play a few games. Sometimes there may also be practice games that you can play without paying additional money.

What Casinos Offer Real-Money Live Dealer Roulette?

Since roulette is so popular and online casinos are used by so many people, most of them offer live dealer roulette games. For those who want to play in New Jersey, some of your options include the following:

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You will find additional options in other states, depending on where you are located. Regardless of where you decide to play, this is an immersive experience that replicates a physical casino. What makes them so unique is that you can access this style of gambling from any mobile device.

Fundamentals Of Roulette Strategy

As with any table or card game at a casino, people who play come up with strategies intended to make them more money. Whether these work or not is up for debate, but they can offer a new way to play the game. Most of these strategies are used by experienced players who want to add a new level of excitement to the game.

Best Bets On The Roulette Table

The best bets to make at a roulette table depend on what your intentions are. Someone who wants to spend a lot of time playing without losing a lot is going to have a different system than someone who wants to win a ton of money quickly. Those who want to make money fast will want to choose a single number and hope for some good luck.

On the other hand, those who want to simply play a lot might want to choose even money bets. You aren’t going to win as much money as selecting a single number. However, you are going to win on a much more regular basis. This means putting money back in your pocket so you can keep playing games as long as you like.

Roulette Betting Systems

The most common betting systems for roulette are the martingale and the reverse martingale. With the former method, you choose a table with a small minimum and high maximum bet and make small wagers on even or odd or black or red. When you win, you keep the winnings and the same wager for the next game. If you don’t win, you double down on your bet each game until you do win.

The reverse martingale system is the exact opposite of the above strategy. Rather than adding to your bets when you lose, you increase them upon winning and lower them if you lose. The idea is that you can keep your money flowing when you are on a streak and prevent losing a lot when things aren’t going so hot.

Roulette: The Five Minute Guide

We mentioned that roulette is a straightforward table game to play for those who are interested in casino gaming. It consists of a wheel with many numbered slots along with a dealer who spins the wheel and ball before it lands into one of the slots. Many bets can be made based on where the ball will end up when the wheel stops.

Basic Rules Of Roulette

When playing roulette in a physical casino, it’s a hands-on experience. Players mark the felt table with markers or chips to indicate their bet. Rather than having a denomination on the chips, they will come in various colors that each indicates a specific amount. For example, a player might exchange $20 for ten $2 markers or four $5 chips. When playing online, things are even more straightforward since it’s a matter of tapping on the screen to show what you want to wager.

The American rules for roulette are relatively straightforward and the entire process starts when players make their bets. Players can bet on red or black, odds or evens, the numbers 1 through 18 or 18 through 36, specifics numbers, or a selection of numbers. The odds of winning vary based on what your specific bet is. For example, some of the most common bets have the following odds:

Common Roulette Variations

There are many different variations of roulette besides the American style. For instance, there is European roulette, which has better odds than American roulette. Instead of having a single zero and a double zero on the wheel, the European wheel has only a single zero. This gives players an advantage since any time the ball lands on a zero or double zero, the house wins.

French roulette is another variation that has a single zero on the wheel. However, it also has special rules. One of them is that a player loses half of their bet when the ball lands on zero for outside bets. There is another bet that “imprisons” bets when zero is landed on. Rather than getting half of a bet back, the bet will stand for the next spin.

The House Edge in Roulette

When playing traditional American roulette, the house always has the edge, which means there is a specific probability of winning. All of the casinos in the United States use these rules except for those in Atlantic City, New Jersey. The house edge is going to be 1/19, which is 5.26 percent. The only exception is on a zero, double zero, one, two, three combination, which has an even higher edge at 7.89 percent.

When it comes to Atlantic City, the even money bets are similar to European rules, where a ball that lands on zero or double zero causes players to lose only half of the wager. That brings the house edge down to 2.63% on this kind of bet but does not come into effect on single-zero wheels.

Playing Las Vegas-Style Roulette Online for Free

One of the first places that people think of when it comes to roulette and other table games is none other than Las Vegas. Playing the same kind of roulette that you’ve seen on your television screen in many films and television shows is super appealing to a wide variety of people. The good news is you can do so right from your own home.

Tropicana Casino is a New Jersey-based casino that offers an online app where you can play a wide variety of slots and table games. This particular casino offers single zero roulette, American roulette, European roulette, as well as a selection of other games. This is also one of few casinos that offer 90 Ball Bingo for those who sign up to play.

Another casino with roulette online from New Jersey is Golden Nugget Casino. When this casino went live in 2016, it started out offering roulette, blackjack, and baccarat games with live dealers. This is a great way to feel like part of the action while playing with other users since it takes part in real-time.

SugarHouse Casino is found in Pennsylvania and is another online legal casino with a selection of roulette games. Traditional roulette, American roulette, and other variations of the game are available for play online. There is a wide selection of tables games online at this casino, but the slot games are where this app shines.

Roulette Games: Single Zero, Double Zero, Triple Zero

You may have heard the terms single zero, double zero, and triple zero in terms of roulette and wondered what the difference between these games is. Besides offering additional zeros on the wheel, some of these games are more fruitful for players than others, which is an important thing to know if you want to win more games.

Which Game Is Best For The Player?

As the number of zeros on a roulette wheel goes up, so does the edge that the house has against a player. Since a ball landing on zero, at least in American roulette, results in players losing, the more zeros there are, the more chances there are to lose. Once you realize that, you’ll find that the best roulette game for players is single zero.

Compare House Edge

To explain a bit more why single-zero games are best for players, we only have to look at the house edge for single, double, and triple zero games. Single zero roulette or European roulette has one zero on the wheel, which has a total of 37 slots. That means the house has an edge of 2.7 percent on every bet.

As we mentioned earlier, American roulette has a house edge of 5.26 percent, which makes it less likely for a player to win. The odds go down even more when playing triple zero roulette, which has three zeros (one is usually a logo of the casino) and 38 slots. Since there are even more zeros where the ball can land, the house edge goes up to 7.69 percent.

Las Vegas Casinos Where You Can Play Single Zero

Many of the casinos in Las Vegas have single zero roulette games, where the person playing has the best chance of winning possible. Some of these include the Bellagio, the MGM Grand, the Wynn, the Mirage, and the Monte Carlo. A selection of these games has French or European rules, while others do not.

Many of the online casinos in Pennsylvania and New Jersey also offer this kind of roulette. A selection of the casinos in New Jersey with this option include Resorts, Caesars, Pala Casino, Golden Nugget, and Tropicana. Other options in the state include Mohegan Sun, Party Poker, Harrah’s, and 888.

For those in Pennsylvania who want to play with established online casinos, choices range from Harrah’s to Parx, SugarHouse, Valley Forge, and more. Hollywood Casino, Presque Isle Downs Casino, and Mount Airy Casino also offer a selection of roulette options.

Free Roulette Online Play FAQ

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Yes. In some cases, you can play a game of free roulette without making an account. However, there are also roulette sites that will want you to register before you play a game. Whatever you prefer to do, you will find a roulette site that offers the option. It’s just a matter of digging into the details to find out what is required.

Yes. Sweepstakes sites offer roulette that can be played for free, but you can also win real money or other prizes. Sites like Chumba Casino are an alternative for those who live in states without legal real money gambling.

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Yes. One of the best ways to get comfortable with roulette betting strategies is by playing free games. You can try new things without the pressure of losing money if the strategy doesn’t go your way. This can also be a great way to try roulette and see if it’s right for you.

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Sometimes. It depends on the site where you are playing to play free roulette games. Some are going to require a flash player while others may use another type of technology. Make sure to look at the requirements before playing if you want to avoid flash games.