“PROFIT IS NOT A MATTER OF CHANCE; IT IS A MATTER OF CHOICE!”
Most everyone says each and every spin of a roulette wheel is random and independent and has no connection to past or future spins. Because it is a 'replacement' game the odds of the number hitting again remain the same after each spin, so you cannot give any weight to the past or future numbers."
The usual argument is that the "wheel has no memory". The only thing the so called Professional Gamblers and Mathematicians can point to is the written argument that simply says that each roulette spin is an independent event. Have you seen proof of that? To some it is just logical but to a few they have since stumbled on the truth and are afraid to admit it because they have too much to lose. They are afraid to admit the truth because their credibility goes out the window. However, that approach is very shortsighted, because when the truth comes out they will have a hard time explaining to their public why it took them so long to see it.
I believe that most mathematicians and experienced gamblers have this incorrect mindset.
Mathematicians keep telling us, "Roulette Wheels have no memory, dice have no memory, and tossed coins have no memory because they are inanimate objects." THIS MAY BE TECHNICALLY TRUE BUT IT IS A BIG JUMP FROM HERE TO ASSUMING EACH EVENTS INDEPENDENCE AND THAT A SYSTEM CAN’T BE FOUND. The roulette wheel is designed to be mechanically “perfect”, the purpose of which is to generate random numbers evenly, fairly, and without bias. If in fact, ALL numbers have the SAME chance of coming out of this perfection then EACH number is treated EQUALLY and therefore will / must be delivered EVENLY over the long term. If so, then the wheel must have a Mechanical sort of Memory. The “Law of Averages” can only produce truly random results in an unbiased atmosphere.
The greatest ignorance is to reject something you know nothing about." --Horace Greeley Casinos work very hard to insure Roulette wheels are random, so why not make sure we design a system that works around random. The level of perfection in the wheel itself is what determines whether the LoA is applicable, or not. The more precise the device, the more precise the random table results will be. Therefore, a roulette wheel while supposedly random produces somewhat predictable results. Predictable meaning the LoA will affect will come out. That being so then we should play to the ODDS. Since the results are somewhat predictable, then random in Roulette does not mean independent. Random would mean independent if the numbers to choose from were “Infinite” however since we are using a specific grouping of numbers (00, or 0 to 36) then each spin is not totally independent. It is dependant on a limited series of 37 or 38 numbers and therefore dependant on the “Law of Averages” that every number in that specific group that hasn’t shown lately will eventually show up sooner and all numbers over time come out 1 in 37 or 38 spins as long as there is no bias influence.
If a 37 number Roulette wheel is spun once, there are 37 possible outcomes—1 to 37. Since any number is as likely to turn up as the other, these outcomes are called equally likely outcomes. Probability or the Odds are expressed as the ratio of favorable outcomes to the total number of equally likely outcomes. So the probability of obtaining any number is 1:37— that is, 1 to 37, or 1/37. This probability does not mean that all 37 numbers will always occur once in every 37 spins; it means that each number is likely to occur on average once in every 37 spins. This is what is known as “The Law of Averages”, and it dictates a statistical pressure on trends to even out results. Trends are deceptive and sometimes difficult to perceive. Trends interfere with the Law of Averages; however, they both can work for you if you know how to deal with them. Understanding the LOA and trends guides you to the right choices. You must learn to be patient and very disciplined Since any good system is based on mathematics and since we play with groupings of #’s, we can predict with some measure of success the wins and losses. The fact that Roulette is totally random, this in and of itself somewhat allows for predictability.
Stop and really think about this next sentence…. "If each spin is independent then how do things even out over time?" A numbers ability to appear on average 1 in 37 / 38 spins requires that its appearance either speed up or slow down over time as all other numbers thru each numbers natural statistical pressure also influence the average distribution of all numbers.
There is dependence. The dependence is on an unbiased wheel, and each number. The fact that we know that #’s appear on average 1 in 37/38 spins is something to build a system on.
While the use of the words Mechanical Memory is a “Big Pill” to swallow, we feel it very
appropriate considering all numbers will even out over time in an unbiased atmosphere with an unbiased wheel. If the wheel was biased things would not even out. On the other hand we do not think what it’s called is as important as what it produces. What is more important is that an unbiased wheel, through the “Law of Averages”, its numbers are influenced to even out over time. This only proves that all numbers are dependant on each other.
There are a very few who agree the wheel has any kind of a memory no less a mechanical memory. However, we have carried it a step further and this new school of thought is that you can assign weight to past outcomes to predict to SOME degree of accuracy the outcome of future spins. Something very similar to card counting without the cards. We are not talking about being telepathic. We are talking about playing to the odds. An important fact and despite what so called experts say, you actually will find that in roulette, previous numbers (both the ones that have hit and especially the ones that have not) have an important bearing on what is going to happen on future spins.
The self professed professionals, “ad nausium”, carry this a step further and continue to state as a fact that a winning system is not a winning system if it cannot hold up to and profit by thousands of spins. (Computer or otherwise). Systems do not have to withstand a million spins and rake in 2 million dollars to be a winning system. If you look at Systems that way you will never ever win. However, change your expectations of their outcome and your opinion of systems will change. There is nothing like walking up to a table, playing for 6 to 15 spins and walk away with 15 or 20 chips to change ones attitude about systems. 20 $1chips = $20, 20 $5 chips = $100, and 20 $25 chips = $500. What is that wood?

HOWEVER, NO STRATEGY SURVIVES COMPLETELY ITS CONTACT WITH A WHEEL. EVERY TABLE IS TOTALLY INDEPENDENT AND EVERY TABLE ACTS ANY WAY IT WANTS.
THEREFORE NO MECHANICALLY SET STRATEGY WE KNOW OF WILL WORK ALL THE TIME.

What they totally neglect and ignore to take into account is our own ability to make conscious decisions during play which can enhance our ability to win.
While many will not agree, let’s look at an example of the dozens. Each dozen has the probability of coming out once in 3.167 spins. We all know it rarely does short term. However, if I (speaking for myself) were on a table with a charting board and found that the 3rd dozen hasn’t hit let’s say in the last 15 to 20 spins, I would certainly consider covering the high numbers 25 to 36. Why? Because it is PAST DUE! Have you ever heard of the term PAST DUE? Have you ever used the term PAST DUE? PAST DUE means something is waited (due) to come in. It is exactly these kinds of intelligent decisions that we can bring to the table along with a good system that help carry us over the edge. So a system CAN win and NOT be mechanical.
Those who have played any specific system for let’s say thousands of spins will recall a point in time at which the system opened up to you. You at that point can see clearly see its short comings. That being the case and depending on the system you could “ADAPT”. We can bring our skill, knowledge, and discipline to the table to modify and continually improve the system.
 In addition, if you keep track of the outcomes, that information is helpful on your decisions in what numbers or groups of numbers to play next or more importantly not play next. When you skip betting locations you not only save money but your net profit is higher also. A human being playing roulette can use his or her intelligence & memory to observe and chart a "connection" between past and future spins that can be used to create a system that is applicable on roulette wheels to predict the likely hood on the next outcome. Not the next # but possibly the next group. An extended famine of high numbers (for example) provides a solid betting opportunity to cover those numbers after that absence, provided the wheel is not biased.
We also have to be able to figure a way to predict (I hate using that word) what will not come out, not every time but with enough success to keep us ahead of the casino. Most gamblers are trying to figure out what should come out. You have a better shot at figuring out what will not come out. Lets fact it it's 36 or 37 chances it won’t to 1 it will come out, it’s a “No Brainer”. Chose not to bet what will not come out, how could you lose? It is more simply another way of playing “To the Odds”. Will you be successful all the time? Absolutely not, however all you need develop is skill enough to be successful
once in awhile and only enough to keep you ahead of the Casino. And if you are playing a system that plays close to the casino’s edge then you won’t need much to stay ahead of them.

A System doesn’t work by just getting on a table and the money starts rolling in. Systems don’t work that way. They are designed to bring you;
1. Close to the House edge;
2. Help you manage your money to maximize wins and minimize losses;
3. Gives you the staying power for the good runs and allows you time to bring your special
techniques to the table;
4. Basically it’s a guide for you through the various methods and a way to just avoid random
betting which rarely ever works.
5. Systems help you establish your win / walk goals and stop losses.
6. Systems allow you the time to employ you knowledge.
You can’t be impatient, the numbers don’t always come out the way they are so called, “suppose to”. A good system and good decisions keep you there long enough to get ahead of the casino.
When you add up ALL together these little edges that you personally bring to the table, you can stay ahead of the casino. It’s these personal extra edges / advantages that we can bring to the table that turns a good mechanical system into a long term winning system. But these extras are very difficult and in some cases impossible to program into a computer which when played could actually prove the system wins long term.
Casinos work very hard to insure Roulette wheels are random, so why not make sure we design a system that works around random. The level of perfection in the wheel itself is what determines whether the LoA is applicable, or not. The more precise the device, the more precise the random table results will be. Therefore, a roulette wheel while supposedly random produces somewhat predictable results. Predictable meaning the LoA will affect will come out. That being so then we should play to the ODDS. Since the results are somewhat predictable, then random in Roulette does not mean independent. Random would mean independent if the numbers to choose from were “Infinite” however since we are using a specific grouping of numbers (00, or 0 to 36) then each spin is not totally independent. It is dependant on a limited series of 37 or 38 numbers and therefore dependant on the “Law of Averages” that every number in that specific group that hasn’t shown lately will eventually show up sooner and all numbers over time come out 1 in 37 or 38 spins as long as there is no bias influence.
If a 37 number Roulette wheel is spun once, there are 37 possible outcomes—1 to 37. Since any number is as likely to turn up as the other, these outcomes are called equally likely outcomes. Probability or the Odds are expressed as the ratio of favorable outcomes to the total number of equally likely outcomes. So the probability of obtaining any number is 1:37— that is, 1 to 37, or 1/37. This probability does not mean that all 37 numbers will always occur once in every 37 spins; it means that each number is likely to occur on average once in every 37 spins. This is what is known as “The Law of Averages”, and it dictates a statistical pressure on trends to even out results. Trends are deceptive and sometimes difficult to perceive. Trends interfere with the Law of Averages; however, the both can work for you if you know how to deal with them. Understanding the LOA and trends guides you to the right choices. You must learn to be patient and very disciplined.

There are three types of trends for you to recognize.
1) ALTERNATING TRENDS – for example; colors, odd, even, high or low ALTERNATE when they come out.
4) GROUP TRENDS - There will be times when a GROUP of one will come out then a GROUP of the other.
5) NO TRENDS - There will be times when NO PATTERN (trend) is visible. This believe it or not is a trend. This is what makes trends so difficult to spot.

Just because we don’t recognize a trend doesn’t mean it isn’t a trend. When we see a full house in cards we assign a specific value to it. When we see for example 3, 5, 7, 8, 10 we don’t assign a value to it but it is also a specific trend. It’s just that one is more recognizable and we place more value and a specific title on one and not the other. Trends in Roulette can be even more difficult to distinguish.
The numbers do not come out in any specific order they come out randomly and / or in trends / groupings. Trends and even severe anomalies happen on occasion. These sever anomalies do not prove independence but they lead many to believe in independence. However, as time goes by the “Law of Averages” will fulfill its destiny as there is a natural statistical propensity sometimes called a mathematical weight placed on numbers that have been shy. It is this weight that we place on these shy numbers that lead us to make educated decisions / choices to bet or not bet a number or group of numbers. It is this statistical pressure that evens things out over time.
We always knew the Law of Averages existed and knew things evened out in time. We all know this from childhood with respect to the toss of a coin. So we focused on figuring out “Not why” but a way to predict it with some reasonable accuracy. We tried everything. For years...we killed forest after forest with paper graphs and computer runs. Our focus was very simple, find the closest system to the houses edge. Well after years we did just that. Then we had to use knowledge, discipline, experience to do what can't be done by mechanical computers and that is make choices.

System playing is a tool or a weapon. Like all weapons you should know all about them, how to use them and practice, practice and practice any system before going to the table.
The only reason our system does work is because the Gamblers Fallacy is a Fallacy. Roulette events are not independent and depending on the system, they are somewhat predictable. When you finally see a system that works you also see proof that the wheel has a memory, as bad as it may be, it still has a memory. Of course not in the truest sense, however a type of mechanical memory which is the only reason why we could design a system that would or could work. This was the reason we were able to take advantage of the Law of Averages. The Barbi Systems work not only because we utilize our brains and skill as well as it’s unique money management system, but because we’ve taken a # of money management events and strung them together in an effort to minimize risk and overcome the effect of the House edge / cut. To win you must utilize every little advantage available. One of the reasons the Barbi systems succeed in staying ahead of the casino is because we understand and know how to manage what can be called Roulette’s 37/38 number statistical propensity. It’s that Law of Average’s natural pressure which compels gaming decisions to ultimately conform to their statistical expectation. When we understand it, we can on occasion make the right choice.

THE LAW OF AVERAGES PLAYS A BIG ROLL IN WHAT EVENTUALLY COMES OUT.
EVENTUALLY IS A KEY WORD HERE. HOW LONG IS EVENTUALLY? LONGER THAN YOU AND WE HAVE THE MONEY TO WAIT FOR. NEVER CHASE #S OR COLORS. UNDERSTANDING THE LAW OF AVERAGES WILL HELP IN UNDERSTANDING ROULETTE.

Based on the Law of Averages what are the odds of a pre picked # coming out,
The first time = 38 to 1
Back to Back = 38X 38 = 1,444 to 1
Three #s in a row = 38X38X38= 54,872 to 1
Four #s in a row 38X38X38X398 = 2,085,136 to 1
Five #s in a row = 38X38X38X38X38 = 79,235,168 to 1
Six #s in a row = 38X38X38X38X38X38 = 3,010,936,384 to 1
Sorry that’s as far as my hand-held calculator can go.
Let's take 1,000,000 spins.
RED will come out ABOUT half the time.
ODD #s will come out ABOUT half the time.
HI & Lo #’s will come out ABOUT half the time.

Of course the 0 and 00 will effect this slightly but eventually every # including 0 and 00 will come out an average of 1 time in 38 spins. The question is how long is eventually? The same color back to back will come out APPROXIMATELY 250,000 times out of 1,000,000 spins.
Three in a row of the same color " " " “ 125,000 " " out of 1,000,000 spins
Four in a row of the same color " " " “ 62,500 " " out of 1,000,000 spins.
Five in a row of the same color " " " “ 31,250 " " out of 1,000,000 spins.
Six in a row of the same color " " " “ 15,625 " " out of 1,000,000 spins.
However, you have to be careful, eventually when reality strikes it’s not always accommodating. For example: RED could come out 556,543 times out of a million and BLACK could come out 443,457 times. That means that BLACK came out 113,106 times less. It could take millions of more spins before they even out. Possibly even more, want to wait?
They keep saying red and black have an even chance of coming out. Let’s look at the wheel. Red / Black / Red / Black etc all around the wheel. Now let’s imagine red has come out 10 times in a row….no let’s say 20 reds in a row. While the odds are even because of the spacing, the probability is that Black is due to even things out. When the majority of people realize this the casinos will have a problem. All the big shots get the odds and the probability mixed up. The other names for it are sequential probability and absolute probability

Some interesting statistics:
In 1959 At the El San Juan Hotel in Puerto Rico the #10 came out six times in a row. The probability of that happening is 1 in 3,010,936,384 that’s 1 in 3 billion + chances.
Some other Interesting statistics are what I and a couple of friends have seen come  out.
Once I heard the 2nd Dozen came out 15 times in a row. Runs of 7 to 10 of a dozen or column in a row are not that uncommon and will usually occur at least twice in a thousand spins and sometimes even more.
A friend has seen 5 zero/double zero's come up in a row and on another occasion 6 out of 8 spins were either zero or double zero. He also reported 24 reds hit in a row and 22 blacks. By the way, would you have bet the opposite color when these streaks ended? If you did, you would still have lost money.
The same color continued to dominate over the next dozen spins or so hitting at least twice as much as the weaker color. I'm sure the other color caught up eventually, but it doesn't have to happen right away. And besides, you don't know how dominate the other color was before you arrived at the table.
When you have a trend that hot, it doesn't usually just cool down all of a sudden and swing back the other way although I've seen that happen as well.
The probability of your birthday coming out:
1 time 1 chance in 38 spins
2 times in a row 1 chance in 1,444 spins
3 times in a row 1 chance in 54,872 spins
4 times in a row 1 chance in 2,085,136 spins
5 times in a row 1 chance in 79,235,168 spins
6 times in a row 1 chance in 3,010,936,384 spins
Yet you’ll bet it over and over again even after it hits! Why?
Did it ever come out two times in a row? In addition, if it did would you bet in again and again?
You have a better chance in hitting the lottery. By MONEY MANAGEMENT, we mean how much you bet, when and what numbers you bet on and when to bet big and when to regress or reduce your bets. That's MONEY MANAGEMENT.

The probability of a color or an odd or even # coming out BACK TO BACK is also risky.
1 time 1 chance out of 18 spins
2 times in a row 1 chance in 36 spins
3 times in a row 1 chance out of 54 spins
4 times in a row 1 chance out of 72 spins
5 times in a row 1 chance out of 90 spins
6 times in a row 1 chance out of 108 spins
7 times in a row 1 chance out of 126 spins
As you can see betting on the same color after it comes out is also risky. I believe the longest Roulette win for a single color bet was 32 Red #s in a row (August 1943 Arrowhead Casino, Saratoga).
My wife could hardly lose a spin one night. She hit 39 times out of 46 spins on inside bets, that’s 7 lost spins with 27 HITS IN A ROW out of the last 28 spins using the INSIDE Barbi System at the Atlantis in Paradise Island, The Bahamas, Feb 98. I don’t know if that was a record but I was impressed.

I know its a old post but I have a BIG calculator and thought I'd add to what RichardGraceFan was saying:

The first time = 38 to 1
Back to Back = 38 x 38 = 1,444 to 1
Three #s in a row = 38 x 38 x 38 = 54,872 to 1
Four #s in a row 38 x 38 x 38 x 38 = 2,085,136 to 1
Five #s in a row = 38 x 38 x 38 x 38 x 38 = 79,235,168 to 1
Six #s in a row = 38 x 38 x 38 x 38 x 38 x 38 = 3,010,936,384 to 1
Seven #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 =  114,415,582,592 to 1
Eight #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 =  4,347,792,138,496 to 1
Nine #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 =  1.65216101 × 10¹⁴to 1
Ten #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 = 6.27821185 × 10¹⁵ to 1
Eleven #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 = 2.3857205 × 10¹⁷ to 1
Twelve #s in a row = 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 x 38 = 9.06573791 × 10¹⁸ to 1


Regards Rick lol

Lol, says who?

A random walk is a mathematical term used to describe a process where each trial is random and independent from anything that came before it.

hxxp: en. wikipedia. org/wiki/Random_walk

I don't know where the one who wrote this nonsense is from, but in this world you can't use the Law of Averages to increase your chances of winning betting on true random events.  This fact is verifiable.

fender,

I agree with you to some extend. However beating roulette is not easy at all. The problem is that the "percentages" as you call them, or expected appearances, do not "correct" themselves always very soon. it is ossible fter 100 spins one of the 3 dozens to still be very short of the expected percentages. Yes, at some point it will correct but it could take some time (and a BIG bankroll) for this to happen.

How you came to those conclusions/assumptions is beyond me.

1) Are you able to define the difference between a "chaotic system" and a "random walk"?

The weather is a chaotic system.
Roulette Red/Black outcomes are a simple random walk (the same with coin toss outcomes and lottery results).

2) The fact that each number has precisely the same chance is what makes the game random. In the long run, you get a Gaussian (bell-shaped) distribution of events, which is the main characteristic of a random process.

3) This is not exclusive to roulette randomness, but every simple random process in existence. e.g. coin tosses, lottery results, distribution of rain drops, etc.

You probably assumed that since you get such a nice looking long-term distribution then the game must be non-random.

It's called the gambler's fallacy.