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It can be easily demonstrated that this payout formula would lead to a zero expected value of profit if there were only 36 numbers.
Having 37 or more numbers gives the casino its edge. Note also that 0 and 00 are not odd or even, or high or low. En prison rules, when used, reduce the house advantage.
The house average or house edge or house advantage also called the expected value is the amount the player loses relative for any bet made, on average.
The expected value is:. The presence of the green squares on the roulette wheel and on the table is technically the only house edge.
Outside bets will always lose when a single or double zero comes up. The only exceptions are the five numbers bet where the house edge is considerably higher 7.
This is commonly called the "la partage" rule, and it is considered being the main difference of European and French roulette. There is also modification of this rule, which is called " en prison " rule.
These rules cut the house edge into half 1. The house edge should not be confused with the "hold". The hold is the average percentage of the money originally brought to the table that the player loses before he leaves—the actual "win" amount for the casino.
This reflects the fact that the player is churning the same money over and over again. In the early frontier gambling saloons, the house would set the odds on roulette tables at 27 for 1.
Today most casino odds are set by law, and they have to be either 34 to 1 or 35 to 1. As an example, we can examine the European roulette model, that is, roulette with only one zero.
The rules of European roulette have 10 types of bets. For similar reasons it is simple to see that the profitability is also equal for all remaining types of bets.
In reality this means that, the more bets a player makes, the more he is going to lose independent of the strategies combinations of bet types or size of bets that he employs:.
Here, the profit margin for the roulette owner is equal to approximately 2. Nevertheless, several roulette strategy systems have been developed despite the losing odds.
These systems can not change the odds of the game in favor of the player. Although most often named "call bets" technically these bets are more accurately referred to as "announced bets".
The legal distinction between a "call bet" and an "announced bet" is that a "call bet" is a bet called by the player without him placing any money on the table to cover the cost of the bet.
In many jurisdictions most notably the United Kingdom this is considered gambling on credit and is illegal in some jurisdictions around the world.
An "announced bet" is a bet called by the player for which he immediately places enough money to cover the amount of the bet on the table, prior to the outcome of the spin or hand in progress being known.
There are different number series in roulette that have special names attached to them. Most commonly these bets are known as "the French bets" and each covers a section of the wheel.
For the sake of accuracy, zero spiel, although explained below, is not a French bet, it is more accurately "the German bet".
Players at a table may bet a set amount per series or multiples of that amount. The series are based on the way certain numbers lie next to each other on the roulette wheel.
Not all casinos offer these bets, and some may offer additional bets or variations on these. The series is on a single-zero wheel.
Nine chips or multiples thereof are bet. Two chips are placed on the trio; one on the split; one on ; one on ; one on ; two on the corner; and one on Zero game, also known as zero spiel Spiel is German for game or play , is the name for the numbers closest to zero.
All numbers in the zero game are included in the voisins, but are placed differently. The numbers bet on are The bet consists of four chips or multiples thereof.
Three chips are bet on splits and one chip straight-up: This type of bet is popular in Germany and many European casinos. It is also offered as a 5-chip bet in many Eastern European casinos.
As a 5-chip bet, it is known as "zero spiel naca" and includes, in addition to the chips placed as noted above, a straight-up on number This is the name for the 12 numbers that lie on the opposite side of the wheel between 27 and 33, including 27 and 33 themselves.
On a single-zero wheel, the series is Very popular in British casinos, tiers bets outnumber voisins and orphelins bets by a massive margin.
Six chips or multiples thereof are bet. One chip is placed on each of the following splits: The tiers bet is also called the "small series" and in some casinos most notably in South Africa "series ".
A variant known as "tiers " has an additional chip placed straight up on 5, 8, 10, and 11m and so is a piece bet.
In some places the variant is called "gioco Ferrari" with a straight up on 8, 11, 23 and 30, the bet is marked with a red G on the racetrack.
These numbers make up the two slices of the wheel outside the tiers and voisins. They contain a total of 8 numbers, comprising and Five chips or multiples thereof are bet on four splits and a straight-up: A number may be backed along with the two numbers on the either side of it in a 5-chip bet.
For example, "0 and the neighbors" is a 5-chip bet with one piece straight-up on 3, 26, 0, 32, and Neighbors bets are often put on in combinations, for example "1, 9, 14, and the neighbors" is a chip bet covering 18, 22, 33, 16 with one chip, 9, 31, 20, 1 with two chips and 14 with three chips.
Any of the above bets may be combined, e. Final 4, for example, is a 4-chip bet and consists of one chip placed on each of the numbers ending in 4, that is 4, 14, 24, and Final 7 is a 3-chip bet, one chip each on 7, 17, and Final bets from final 0 zero to final 6 cost four chips.
Final bets 7, 8 and 9 cost three chips. Some casinos also offer split-final bets, for example final would be a 4-chip bet, one chip each on the splits , , , and one on A complete bet places all of the inside bets on a certain number.
Full complete bets are most often bet by high rollers as maximum bets. The maximum amount allowed to be wagered on a single bet in European roulette is based on a progressive betting model.
For instance, if a patron wished to place a full complete bet on 17, the player would call "17 to the maximum".
To manually place the same wager, the player would need to bet:. The player calls his bet to the croupier most often after the ball has been spun and places enough chips to cover the bet on the table within reach of the croupier.
The croupier will immediately announce the bet repeat what the player has just said , ensure that the correct monetary amount has been given while simultaneously placing a matching marker on the number on the table and the amount wagered.
Based on the location of the numbers on the layout, the number of chips required to "complete" a number can be determined.
Most typically Mayfair casinos in London and other top-class European casinos with these maximum or full complete bets, nothing except the aforementioned maximum button is ever placed on the layout even in the case of a win.
Experienced gaming staff, and the type of customers playing such bets, are fully aware of the payouts and so the croupier simply makes up the correct payout, announces its value to the table inspector floor person in the U.
There are also several methods to determine the payout when a number adjacent to a chosen number is the winner, for example, player bets 40 chips on "23 to the maximum" and number 26 is the winning number.
The most notable method is known as the "station" system or method. When paying in stations, the dealer counts the number of ways or stations that the winning number hits the complete bet.
In the example above, 26 hits 4 stations - 2 different corners, 1 split and 1 six-line. The dealer takes the number 4, multiplies it by 30 and adds the remaining 8 to the payout: If calculated as stations, they would just multiply 4 by 36, making with the players bet down.
Over the years, many people have tried to beat the casino, and turn roulette—a game designed to turn a profit for the house—into one on which the player expects to win.
All betting systems that rely on patterns, when employed on casino edge games will result, on average, in the player losing money.
Certain systems, such as the Martingale, described below, are extremely risky, because the worst-case scenario which is mathematically certain to happen, at some point may see the player chasing losses with ever-bigger bets until he runs out of money.
The American mathematician Patrick Billingsley said  that no betting system can convert a subfair game into a profitable enterprise.
At least in the s, some professional gamblers were able to consistently gain an edge in roulette by seeking out rigged wheels not difficult to find at that time and betting opposite the largest bets.
Whereas betting systems are essentially an attempt to beat the fact that a geometric series with initial value of 0. Thorp the developer of card counting and an early hedge-fund pioneer and Claude Shannon a mathematician and electronic engineer best known for his contributions to information theory built the first wearable computer to predict the landing of the ball in This system worked by timing the ball and wheel, and using the information obtained to calculate the most likely octant where the ball would fall.
Ironically, this technique works best with an unbiased wheel though it could still be countered quite easily by simply closing the table for betting before beginning the spin.
In , several casinos in Britain began to lose large sums of money at their roulette tables to teams of gamblers from the USA.
Upon investigation by the police, it was discovered they were using a legal system of biased wheel-section betting.
As a result of this, the British roulette wheel manufacturer John Huxley manufactured a roulette wheel to counteract the problem.
The new wheel, designed by George Melas, was called "low profile" because the pockets had been drastically reduced in depth, and various other design modifications caused the ball to descend in a gradual approach to the pocket area.
Thomas Bass , in his book The Eudaemonic Pie published as The Newtonian Casino in Britain , has claimed to be able to predict wheel performance in real time.
The book describes the exploits of a group of University of California Santa Cruz students, who called themselves the Eudaemons , who in the late s used computers in their shoes to win at roulette.
In the early s, Gonzalo Garcia-Pelayo believed that casino roulette wheels were not perfectly random , and that by recording the results and analysing them with a computer, he could gain an edge on the house by predicting that certain numbers were more likely to occur next than the 1-in odds offered by the house suggested.
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