Calculus of Variations

That means Evolution will be breaking grounds and shaping up the future of gaming in this South-Eastern country mostly known as the home of Count Dracula. The odds of winning are always the same. Nine chips or multiples thereof are bet. In the early frontier gambling saloons, the house would set the odds on roulette tables at 27 for 1. It is also offered as a 5-chip bet in many Eastern European casinos. Five chips or multiples thereof are bet on four splits and a straight-up: Tue Sep 25

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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 11; 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. The player's wagered 40 chips, as with all winning bets in roulette, are still his property and in the absence of a request to the contrary are left up to possibly win again on the next spin. 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.

Also typically at this level of play house rules allowing the experienced croupier caters to the needs of the customer and will most often add the customer's winning bet to the payout, as the type of player playing these bets very rarely bets the same number two spins in succession.

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. Most of the time this comes down to the use of betting systems, strategies which say that the house edge can be beaten by simply employing a special pattern of bets, often relying on the " Gambler's fallacy ", the idea that past results are any guide to the future for example, if a roulette wheel has come up 10 times in a row on red, that red on the next spin is any more or less likely than if the last spin was black.

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 [10] 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. This is an updated and improved version of Edward O Thorp 's approach, where Newtonian Laws of Motion are applied to track the roulette ball's deceleration; hence the British title. 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.

This he did at the Casino de Madrid in Madrid , Spain , winning , euros in a single day, and one million euros in total. Legal action against him by the casino was unsuccessful, it being ruled that the casino should fix its wheel. To defend against exploits like these, many casinos use tracking software, use wheels with new designs, rotate wheel heads, and randomly rotate pocket rings.

At the Ritz London casino in March , two Serbs and a Hungarian used a laser scanner hidden inside a mobile phone linked to a computer to predict the sector of the wheel where the ball was most likely to drop. The numerous even-money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a martingale betting strategy , wherein the gambler doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet.

The problem with this strategy is that, remembering that past results do not affect the future, it is possible for the player to lose so many times in a row, that the player, doubling and redoubling his bets, either runs out of money or hits the table limit. A large financial loss is certain in the long term if the player continued to employ this strategy. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence.

Regardless of the specific progression, no such strategy can statistically overcome the casino's advantage, since the expected value of each allowed bet is negative. The Labouchere System involves using a series of numbers in a line to determine the bet amount, following a win or a loss. Typically, the player adds the numbers at the front and end of the line to determine the size of the next bet.

When he wins, he crosses out numbers and continues working on the smaller line. If he loses, then he adds his previous bet to the end of the line and continues to work on the longer line. This is a much more flexible progression betting system and there is much room for the player to design his initial line to his own playing preference.

This occurs because as the player loses, the average bet size in the line increases. The system, also called montant et demontant from French, meaning upwards and downwards , is often called a pyramid system. It is based on a mathematical equilibrium theory devised by a French mathematician of the same name.

Like the martingale, this system is mainly applied to the even-money outside bets, and is favored by players who want to keep the amount of their bets and losses to a minimum. The betting progression is very simple: After each loss, you add one unit to the next bet, and after each win, one unit is deducted from the next bet.

Starting with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. If this is followed by a win, the next bet would be 1 units. This betting system relies on the gambler's fallacy—that the player is more likely to lose following a win, and more likely to win following a loss.

There are numerous other betting systems that rely on this fallacy, or that attempt to follow 'streaks' looking for patterns in randomness , varying bet size accordingly. Many betting systems are sold online and purport to enable the player to 'beat' the odds. From Wikipedia, the free encyclopedia. This article is about the casino game.

For other uses, see Roulette disambiguation. Massachusetts Institute of Technology. Retrieved 20 October The theory of gambling and statistical logic 2nd ed. The Modern Pocket Hoyle: Probability and Measure 2nd ed.

Advantage Play for the Casino Executive. Science The Guardian , guardian. Retrieved 18 January Retrieved 09 June Gambling mathematics Mathematics of bookmaking Poker probability. Casino game Game of chance Game of skill List of bets. Category Commons Wiktionary WikiProject. Retrieved from " https: Gambling games Roulette and wheel games.

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Views Read Edit View history. In other projects Wikimedia Commons. This page was last edited on 18 September , at Bingo is one of the oldest of the bunch and is popular between people of all ages nowadays. It may not be the quickest way to win money, but playing bingo, you can rip a huge jackpot.

Keno — this is one of the oldest gambling. It is known that Chinese emperors of the Han dynasty staged drawings, similar to the modern keno lottery to raise money to maintain the army. Makes sense if anything. Mathematicians say that a deck of 52 playing cards can form a 2,, unique combinations.

So, the probaility to get a pair in combination is It does not matter on what basis the player crossed out the number. The odds of winning are always the same. Lottery — is a game based on luck. According to statistics 6. Damn it girls, you gotta catch up!

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