Editing Roulette (section)

==Betting strategies and tactics==
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.<ref name=WizardOfOdds>{{cite web|url=https://wizardofodds.com/gambling/betting-systems/|title=The Truth about Betting Systems|publisher=wizardofodds.com|date=15 June 2019|access-date=22 September 2020}}</ref> In practice, players employing betting systems may win, and may indeed win very large sums of money, but the losses (which, depending on the design of the betting system, may occur quite rarely) will outweigh the wins. 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 they run out of money.

The American mathematician Patrick Billingsley said<ref>{{cite book |last=Billingsley |first=Patrick |author-link=Patrick Billingsley  |title=Probability and Measure |url=https://archive.org/details/probabilitymeasu00bill_833 |url-access=limited |year=1986 |publisher=John Wiley & Sons Inc. |edition=2nd |page=[https://archive.org/details/probabilitymeasu00bill_833/page/n105 94]|isbn=9780471804789 }}</ref>{{Unreliable source?|date=August 2012}} that no betting system can convert a subfair game into a profitable enterprise. At least in the 1930s, 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.

===Prediction methods===

Whereas betting systems are essentially an attempt to beat the fact that a geometric series with initial value of 0.95 (American roulette) or 0.97 (European roulette) will inevitably over time tend to zero, [[engineer]]s instead attempt to overcome the house edge through predicting the mechanical performance of the wheel, most notably by [[Joseph Jagger]] at [[Monte Carlo]] in 1873. These schemes work by determining that the ball is more likely to fall at certain numbers. If effective, they raise the return of the game above 100%, defeating the betting system problem.

[[Edward O. 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 1961. This system worked by timing the ball and wheel, and using the information obtained to calculate the most likely [[octant (plane geometry)|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 1982, several casinos in Britain began to lose large sums of money at their roulette tables to teams of gamblers from the US. 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. In 1986, when a professional gambling team headed by [[Billy Walters (gambler)|Billy Walters]] won $3.8 million using the system on an old wheel at the [[Golden Nugget Atlantic City (1980-1987)|Golden Nugget]] in [[Atlantic City]], every casino in the world took notice, and within one year had switched to the new low-profile wheel.

[[Thomas Bass]], in his book ''[[The Eudaemonic Pie]]'' (1985) (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 1970s 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.

To defend against exploits like these, many casinos use tracking software, use wheels with new designs, rotate wheel heads, and randomly rotate pocket rings.<ref>{{cite book|last1=Zender|first1=Bill|title=Advantage Play for the Casino Executive|date=2006}}</ref>

At the [[The Ritz Hotel, London|Ritz London]] casino in March 2004, two Serbs and a Hungarian used a [[laser scanning|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. They netted £1.3m in two nights.<ref>[https://www.theguardian.com/science/2004/mar/23/sciencenews.crime The sting: did gang really use a laser, phone and a computer to take the Ritz for £1.3m? | Science | The Guardian<!-- Bot generated title -->], guardian.co.uk</ref> They were arrested and kept on police bail for nine months, but eventually released and allowed to keep their winnings as they had not interfered with the casino equipment.<ref>{{cite book|last1=du Sautoy|first1=Marcus|title=The number mysteries : a mathematical odyssey through everyday life|date=2011|publisher=Palgrave Macmillan|location=New York|isbn=978-0230113848|page=237|edition=1st Palgrave Macmillan}}</ref>

===Specific betting systems===

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 (roulette system)|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 their bets, either runs out of money or hits the table limit. A large financial loss is almost certain in the long term if the player continues 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.

===Types of betting system===

Betting systems in roulette can be divided in to two main categories:

[[File:Martingale System Simulation.png|thumb|Negative progression system (e.g. Martingale)]]

''Negative progression'' systems involve increasing the size of one's bet when they lose. This is the most common type of betting system. The goal of this system is to recoup losses faster so that one can return to a winning position more quickly after a losing streak. The typical shape of these systems is small but consistent wins followed by occasional catastrophic losses. Examples of negative progression systems include the Martingale system, the Fibonacci system, the Labouchère system, and the d'Alembert system.

[[File:Paroli System Simulation.png|thumb|Positive progression system (e.g. Paroli)]]

''Positive progression'' systems involve increasing the size of one's bet when one wins. The goal of these systems is to either exacerbate the effects of winning streaks (e.g. the Paroli system) or to take advantage of changes in luck to recover more quickly from previous losses (e.g. Oscar's grind). The shape of these systems is typically small but consistent losses followed by occasional big wins. However, over the long run these wins do not compensate for the losses incurred in between.<ref>{{cite web|title=Roulette Systems|url=https://www.roulettestar.com/systems/|website=roulettestar.com|access-date=26 February 2021}}</ref>

===Reverse Martingale system===
The Reverse Martingale system, also known as the Paroli system, follows the idea of the [[martingale (roulette system)|martingale betting strategy]], but reversed. Instead of doubling a bet after a loss the gambler doubles the bet after every win. The system creates a false feeling of eliminating the risk of betting more when losing, but, in reality, it has the same problem as the [[Martingale (betting system)|martingale]] strategy. By doubling bets after every win, one keeps betting everything they have won until they either stop playing, or lose it all.

===Labouchère system===
{{Main|Labouchère system}}
The Labouchère System is a progression betting strategy like the [[Martingale (betting system)|martingale]] but does not require the gambler to risk their stake as quickly with dramatic double-ups. 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. If the player wins, they cross out numbers and continue working on the smaller line. If the player loses, then they add their previous bet to the end of the line and continue 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 their initial line to their own playing preference.

This system is one that is designed so that when the player has won over a third of their bets (less than the expected 18/38), they will win. Whereas the martingale will cause ruin in the event of a long sequence of successive losses, the Labouchère system will cause bet size to grow quickly even where a losing sequence is broken by wins. This occurs because as the player loses, the average bet size in the line increases.

As with all other betting systems, the average value of this system is negative.

===D'Alembert system===
The system, also called {{Lang|fr|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 [[Jean le Rond d'Alembert|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, one unit is added 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.

===Other systems===
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. One such system was advertised by Jason Gillon of [[Rotherham]], UK, who claimed one could 'earn £200 daily' by following his betting system, described as a 'loophole'. As the system was advertised in the UK press, it was subject to [[Advertising Standards Authority (United Kingdom)|Advertising Standards Authority]] regulation, and following a complaint, it was ruled by the ASA that Mr. Gillon had failed to support his claims, and that he had failed to show that there was any loophole.