# Roulette/Printable version

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Roulette

# History

"Roulette history is hard to come by because the origin of roulette is lost, and there was likely some form of a wheel based game going back almost as far as the origin of the wheel itself. There are stories that the game was invented in China and brought to Europe by traders who were trading with the Chinese.
"Several early versions of a wheel and spinning ball were invented in the 17th and 18th centuries in Europe. The first games that we would recognize as modern roulette were introduced in Paris casinos around the end of the 18th century. This game contained all of the features that we have today with the one exception, the single zero was colored red while the double zero was colored black. This led to some confusion for players and the color green was introduced for the zero and double zero to alleviate the confusion.
"In the mid 19th century the single zero game was invented in France, this reduced the casino's edge thereby increasing the odds of the player. When gambling was outlawed in Germany the inventor of the single zero machine (Louis Blanc) accepted an invitation to go to Monaco to establish and operate a casino. The casino set the standards for roulette in Europe, and roulette remained exclusive to Monte Carlo until 1933. This led to the gambling and resort industry in Monaco as many of Europe's rich were attracted to the luxurious Monte Carlo casino.
"The use of the double zero roulette wheels survived in the United States and is sometimes called the American Wheel. The introduction of the single zero wheel (with better odds for the player) resulted in the demise of the double zero wheels in Europe and has become known as the French Wheel in roulette history.
"In Europe (also Atlantic City in the U.S.) the Casino's offered another refinement to the game that increased the odds yet again for the player, the option of 'En Prison' was offered. With the en prison option if the player has bet an even money bet (Even-Odd, Red-Black, 1-18 or 19-36) and zero or double zero is the next outcome the player has two options:
* 1. The player can 'imprison' the bet. This means the bet stays where it is and the next spin determines if the bet is lost or returned to the player.
* 2. The player may surrender half of the bet."

## References

* ↑ "Roulette history at roulette-gambling.com".
Next | Game Mechanics

# Mechanics

Back | History
All roulette tables deal with only four elements:
* 1. The roulette wheel.
* 2. The roulette table (aka layout).
* 3. The ball. These days the ball is most likely high impact plastic, but originally it was made of ivory. Modern casinos maintain the integrity of their roulette balls with regular magnetic and x-ray exams.
* 4. The chips. Some casinos allow the player to use generic casino chips at the roulette tables, but most require the player to buy in at the table. The croupier has stacks of various colored chips. Usually each player gets a different color to help avoid confusion of bets, and the player can designate the value of the chip. This is particularly interesting because if one does not specify the chips are usually valued at either $1 or the table minimum, however if they player wished for the chips to be worth $0.25, s/he may do so as long as the ‘’’total’’’ wager meets the table minimums for their respective sectors. So even if the table minimum is $1, one could place four $0.25 bets and still be a legal.
All roulette tables operated by a casino have the same basic mechanics:
* There is a balanced mechanical wheel with colored pockets separated by identical vanes and the wheel which spins freely on a supporting post.
* The wheel is held within a wooden frame which contains a track around the upper outer edge and blocks of a variety of designs placed approximately halfway down the face of the frame.
* A plastic or ivory ball is spun in the track in the frame that holds the wheel. As the ball loses momentum the centrifugal force is no longer sufficient to hold the ball in the groove and it falls down the face of the frame. As the ball hits a block its trajectory is randomly altered on all 3 planes (X, Y, and Z) causing the ball to bounce and skip.
* The ball falls onto the spinning wheel and eventually lands into one of the pockets.
* The number of the pocket the ball falls into determines how the bets placed on the layout table are treated.
After this the specifics of individual tables can vary greatly.
Next | Table Layouts

# Mechanics/Table

Back | Other Statistical Systems
The roulette table has a layout printed onto a felt cover. There are generally only two types of layouts:

## American Layout

The American layout reflects the 38 possible numbers on the American wheel. The main difference between this layout and the European layout is that at the top of the numbers there are a 0 and a 00. This layout also has a unique betting option where one can play the 0, 00, 1, 2, and 3 however this only pays out 6:1 making it the only bet on the table where the house edge is greater than 5.263%.

## European Layout

The European (aka French) layout reflects the 37 possible numbers on the European wheel. The main difference besides the lack of the 00 is that European tables will generally allow announced bets. In a casino you would tell the croupier the bet you would like and s/he would take your chips and place them on a special marker area to indicate your bet. This marker area can vary widely among table makers.
The house edge is 2.70% on all bets, except in Europe on even money bets (even/odd, red/black, 1-18/19-36). There, if you place an even money bet and the ball lands on zero, you will not forfeit the bet. Instead, in some casinos you will get half your bet back, while in others your bet will be "imprisoned", meaning your bet will be unchanged but it will have to play the next spin. Either way, the house edge for even money bets is 1.35%, the lowest house edge in any kind of roulette.
This method of betting is especially used if you want to bet on segments of the roulette wheel (see Mechanical Systems). These are the Announce Bets and the chip increments needed:
images to come
work in progress
Next | Wheel Layout

# Mech Sys

Back | Other Statistical Systems
Mechanical systems are systems which rely on the inherent flaws of a roulette wheel as a mechanical device or contiguous number spans across the wheel layout. This is a fundamental difference in strategy between the way that a table game and a computer generates random numbers.
The basic principle underlying mechanical betting systems is exploiting the flaw in the way that the machine generates the numbers. As opposed to an electronic random number generator where any number is theoretically independent of any other number, a wheel is constructed with numbers situated permanently adjacent to one another. Therefore the numbers are not completely independent to one another because if the ball is right on the edge of falling from one cup to another, the number those cups represents are fixed. This can be especially useful when using Table clocking to determine a biased wheel, but as technology is making finding a biased wheel very difficult, the underlying theory is still interesting to consider. These systems are generally reserved for the American tables because it’s next to impossible to create contiguous sets on the European layout. However the casinos have solved this problems and already have special announce bets that can make this process easier.
If the ball is predestined to fall a certain region of the wheel (the 0 pocket for example), and you cover the four numbers to each side of the 0 {12,35,3,26,0,32,15,19,4}, as the ball jostles and bounces it is more likely to land in the pockets immediately next to the number than the other side of the wheel. However covering these numbers, with the same relative return, and without dropping a ton of chips is the challenge. Finding a betting system that most efficiently covers the numbers on the region of the board is the challenge to the mechanical system.
In this author’s opinion, this is the ONLY system worth exploring with real money in a casino – or buy a wheel and try it at home, but as of the time of this writing (2008) good professional 30” wheels cost around $4000, and a 27” around $2000. When one considers some systems can be explored with a bankroll of less than $100, it may be worth hitting a casino first.
What makes this most interesting is that mathematically the odds don’t change. Covering 24 numbers no matter where they are has the same probability as placing a bet which covers the numbers in sequence around the wheel. Perhaps it’s just a visceral reaction, but there have been many times where the ball seems to land in the pocket for the number which was bet only to have it slide one pocket over. I don’t know physics well enough to say if there is any reason why covering a region of numbers on a roulette wheel is more advantageous than not, but it just feels right. Besides the math has proved ineffectual.
There is only one book that I have been able to find which covers this in any great detail; Beating the Casinos at Their Own Game by Peter Svoboda ISBN 0-7570-0005-3. I make direct references to this source only because this particular section of this book is available on Google Books. This book also covers several other games in interesting ways and I highly recommend buying a copy or getting it from the interlibrary loan from your local library.
Mr. Svoboda goes into several systems and makes several interesting points, but one thing which he does not stress is that it is VITAL to find a roulette wheel with the exact same layout order as the one he uses in his book. It is possible that a wheel could look very similar but have a different order to their numbering which would require the player to analyze that particular arrangement and betting strategy. For instance I have seen some antique tables which have a reversed layout where the 2 is on the left of the 0 as opposed to the right, however everything else was in the same order so this may be a moot point.
The thing that I really like is that Mr. Svoboda also makes all of his systems mathematically related to winning percentages, and his strategies cover sectors of the wheel rather than sections of the layout. Additionally they fit within the constraints of the table limits imposed by most US casinos.
I’ll go into this more later.

## Standing Systems

Standing systems (for lack of a better term) are those where the same bet is played on the same locations irregardless of previous wins or losses. This is opposed to progressive systems as described in the next section.

### System 1

On the American layout, the best known contiguous bet combination is based on the center column. That placement covers the span from 23 to 5 (clockwise) with five gaps {0, 7, 9, 23, and 30}, and it only includes two numbers {8 and 29} which are outside the span. This covers a span width of 15 numbers which is almost exactly two fifths of the wheel.
This bet can be played two different ways.
* Place 4 chips on the center column and one chip on each of the numbers in set {0, 7, 9, 28, and 30}
** Return: If the numbers {2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35} hit, then the return is: (4*2)-5=3. If the numbers {0, 7, 9, 28, 30}hit, then the return is: (1*35)-(4+4)=27. If the numbers {00, 1, 3, 4, 6, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 31, 33, 34, 36} hit, then the return is -9.
* Place 1 chip each on two street bets {7, 8, 9} and {28, 29, 30}, and one chip on 0, and two chips on the center column.
** Return: If the numbers {2, 5, 11, 14, 17, 20, 23, 26, 32, 35} hit, then the return is: (2*2)-3=1. If the number {0} hits, then the return is (1*35)-4=31. If the numbers {7, 9}or {28, 30} hit, then the return is: (1*11)-4=7. If the numbers {8 or 29} hit, then the return is ((2*2)+(1*11))-2=13. If the numbers {00, 1, 3, 4, 6, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 31, 33, 34, 36} hit, then the return is -5.

### System 2

This combines two spans to cover 23 of the 38 numbers on the wheel.
* Place 1 chip on each of the 4 street bets {1, 2, 3}, {13, 14, 15}, {22, 23, 24}, and {34, 35, 36}. This is the first span. Place 1 chip on each of the two street bets {4, 5, 6} and {31, 32, 33}, and place 1 chip on each of the two splits {16, 19} and {18, 21}.
** Return: If the numbers {1, 2, 3, 4, 5, 6, 13, 14, 15, 22, 23, 24, 31, 32, 33, 34, 35, 36} hit, then the return is: (1*11)-7=4. If the number {16, 19, 18, 21} hit, then the return is: (1*17)-7=10. If the numbers {0, 00, 7, 8, 9, 10, 11, 12, 17, 20, 25, 26, 27, 28, 29, 30} hit, the return is -8.

## Progressive Systems

Progressive systems change depending on the previous win/loss history. These systems are based upon the mechanical layout as opposed to statistical systems as described in this chapter.

### System 1

Next | Math

# Math

Probability
If one understands the basics of probability theory, then in roulette especially it is very easy to test betting systems mathematically. Here is the step by step logic of applying probability in roulette to the possible outcomes.
First, all the mathematics used here is based on a European single 0 wheel since the house edge is half the American version.
We know that the probability of an event happening is the chances of that event compared to all the possible events. For instance, when you flip a coin there are 2 possible outcomes: heads, tails. If you want to know what is the probability that the coin will come up heads, then that would be: heads / (heads + tails) = 1/2 = .5. Likewise when playing an even money bet at roulette, that option covers 18 of the 37 possible outcomes: 18/37=.48648649.
To find out the effect the odds have on a measurable outcome, we can apply that outcome to all possible results. So if we’re playing $1 on black, then we know that for 18 of 37 outcomes we will net $1 profit, and for 19 of the 37 possible outcomes we will net a $1 loss. ((18/37)*1)+((19/37)*-1)=-.02702703. This shows the house advantage on any single spin applied to your bankroll. We know that if you place $1 on any even number bet on average you will loose almost three cents per spin or $27 over 100 spins.
This is valuable when looking at more complicated betting within the layout of the table. For instance, if you consider on the thirds position that the return is 2:1. Let’s look at the extremes. If you place a bet on one of the three options, then you are obviously playing against probability: 12/37=.32432432 probability to win. If you place $1 on all three of the possible options, then for 36 of 37 numbers you will loose $2, make $2, and have the bet on the winning third returned to you for a net profit of $0. This of course makes no sense at all, but you’ll win almost every time if you’re in it to feel like a winner however if your considering a system you’re trying to make money. If we hedge the single bet with the second possible bet and place $1 on the first two of the thirds, then we cover 24 of 37 numbers 24/37=.64864865. We’re guaranteed to lose one bet, but if the other hits then we make $2, minus the one lost, plus the winning bet returned makes a net profit of $1 – and here’s the kicker – our chance of winning on any single bet is greater than 50% (64.86% to be precise).
We know that roulette is an independently random game where the results of one action does not affect the odds of a second action, so presented like this one might see this a winning system of finding a way to shift the odds in your favor. However if we analyze all the possible outcomes we see that the proposition is a losing one. 24 of 37 possible outcomes net us $1. On 13 of 37 possible outcomes we loose $2. So we plug in our formula: ((24/37)*1)+((13/37)*-2)=-.05405405. This is even worse than playing even money odds.
Now we come full circle. Almost all systems are based on the premise that the likelihood of an event happening repeatedly gets exponentially smaller the more times in a row one seeks that option. Probability will never rule out a roulette table showing the number 36 100 times in a row, but it will tell us exactly how unlikely it is. The premise is that the probability of an event happening once is multiplied by the likelihood of the second event multiplied by the third event and so on. For instance, for a single number to come up 100 times we multiply (1/37)*(1/37)*(1/37)… for one hundred times. This is a tiny number but we can see how fast it adds up:
(1/37)=.02702703
(1/37)*(1/37)=.00073046
(1/37)*(1/37)*(1/37)=.00001974
(1/37)*(1/37)*(1/37)*(1/37)=.00000053
The likelihood of a number coming up four times in a row is only 0.000053%, but it happens. Just go to Global Player Casino and check out the roulette results for the year. But I digress, the strategies say if you chase a loss long enough it won’t lose any more, and systems like the Martingale set it up so that you realize a profit when that condition fails. However, it’s still a losing system because we can plug in our formula to this just as easily as we can plug it into a single event.
But first let’s examine what it is we’re looking at. If we’re analyzing a system there are only two options we’re interested in: win or loss. Let’s not get too complicated and assume that one loss will exit the system and return the player to the starting state such as the Martingale.
If the first spin loses then we go to a second spin, and if the second spin loses then we go to the third and so on. So we know that for however many levels we examine all the preceding spins will be losses. In other words, if 51.4% of spins will lose, then we are looking at 51.4% of 51.4% will lose twice in a row and 48.6% of 51.4% will win on the second round. Therefore, 51.4% of 51.4% of 51.4% will lose thrice, and 48.6% of 51.4% of 51.4% will win.
For a single level we know that the formula is the probability of a win times the net result and the probability of a loss times the net result.
(((18/37)*1)+((19/37)*-1))= -.02702703
To check the second level, the probability of a loss followed by the probability of a win times the net result is compared to two losses and the net result.
(((19/37)*(18/37))*1)+(((19/37)^2)*-2)= -.27757487
To extrapolate the third, fourth, and fifth level:
((((19/37)^2)*(18/37))*1)+(((19/37)^3)*-4)= -.4133615
((((19/37)^3)*(18/37))*1)+(((19/37)^4)*-8)= -.49040931
We can see no matter how far we go on the Martingale system it’s always more likely a losing proposition than a winning proposition, and the deeper one goes the more likely one is to lose a greater sum of money. Of course this isn’t a surprise since the odds are already against us.
More on other systems and hedge betting later.
Any system can be analyzed like this for any game. If the result is positive, the odds are in the player’s favor. If the result is negative you’re trusting Lady Luck. I haven’t found a formula that results in a positive number. Of course, if I had I'd be in a casino right now.
In practice, most betting systems redistribute the amounts of the wins and losses: an increase in the chance of winning is balanced against a greater loss once it does occur, as it will sooner or later. The oldest and most common betting system is the martingale, or doubling-up, system on even-money bets, in which bets are doubled progressively after each loss until a win occurs. This system probably dates back to the invention of the roulette wheel.
Martingale is the most common betting system in roulette. The popularity of this system is due to its simplicity and availability. When playing on Martingale, it creates the deceptive impression of quick and easy wins. The essence of the Martingale roulette game system is as follows: we bet on an even chance of roulette (red-black, even-odd), for example, on "red": we bet on roulette at $ 1; if you lose, we double the bet and bet $ 2. If we lose at roulette, we lose the current bet ($ 2) and the previous bet ($ 1) by an amount of $ 3. If we win, we win $ 4, eg. wins two bets (1 + 2 = $ 3) and we have $ 1 net win from roulette. If you lost at roulette for the second time using the Martingale roulette system, let's double your bet again (it is now $ 4). If we win, we will win back the previous two bets (1 + 2 = $ 3) and the current one ($ 4) from the roulette wheel, and again we win $ 1 against the casino.
This is a well presented maths explanation of the odds against the player when betting at roulette.But it confuses probability with certainty.Probability Theory deals with uncertainty not certainty. Roulette, like all gambling, is a game of chance so , obviously, chance is involved. This does not mean that only chance is involved. If the roulette wheel is random then no one can predict with certainty that we will win or lose. That certainty belongs to astrology not maths. There is no reason why the wheel should not give the same number continuously for a hundred, a thousand or even a million spins if it is truly random; incidentally, unless we are going to live till eternity then "The Long Run" is irrelevant in real time betting. The writer errs when dealing with betting the First and Second dozens together. Using the 1-18 bet we can lower the odds against us. Placing three chips on 1-18 and one chip on the six-line 19-24 benefits us should zero occur whereas betting the two dozens does not. To my mind, there is an all too casual attitude to discussing roulette and this is exemplified in this article.Also- but not here -there is usually a knee-jerk reaction to anyone who rejects the notion that you are certain to lose. Claims of certainty -to win or lose -are unjustifiable where uncertainty clearly reigns. Gambling is Gambling is Gambling .
* ↑ "Roulette Systems". Britannica.com. {{cite web}}: Text "Britannica.com" ignored (help)
* ↑ "Martingale Strategy".