These are the values that need to be calculated:

• Since there are 37 spaces, the probability of a ball landing on one of them is 1/37.
• There are 18 red spaces 18, so the chance of a ball landing on a red is 18/37.
• The black or green spaces equal 20, so the probability that the ball will not land on red is 20/37.

If you bet 1€ on red, and the ball lands on red, you will win it back, and the amount is doubled, so you profit 1€. If you bet 2€ on red, but the ball lands on green or black, you will lose your bet (-2).

Here, ”A” is used as the variable for the calculation to represent your winnings in roulette from red that takes the value of 2€. The probability is 18/37 and will take the -2 value with 20/37 probability. Here is how you should do the roulette probability formula:

P(Red) x A (value for red) + P(Not red) x A (value that is not red) = 18/37 + 2 + 20/37x (-1) = 0.4865.

Interpreting the results of the probability roulette calculator:

You must remember that the expected value’s meaning is used to interpret the results. The value you can expect is like the average measurement. It is an indication of what will happen each time you bet 2€.

Even if you win multiple times consecutively, you will averagely lose 5 cents in the long run while you play. The house advantage comes from the 0 and 00. This is a very small advantage, making it hard to detect, but the house will always win at the end of your game.

You must know that the true odds represent the probability of roulette outcome, rather than the possibility. However, the casino is not going to pay out winnings based on true odds. The winning bets are paid using the 1:35 odds, and the even money wagers have a 1:1 payout. This is because of that one zero pocket.

What is the Probability of Winning at a Roulette Wheel?

These bets are quite different, and they are exclusive to French/European roulette only. The numbers in this wheel are combined based on the roulette wheel’s position instead of the table. There are two kinds – fixed and variable.

Zero’s neighbours – These are bets that cover 17 numbers, and all of those are near green zero. You would have to put at least nine chips so that all those numbers are covered, and you will have winning odds of 45.9%. There is no fixed payout, and it can be as high as 24:1, which depends on the number that wins. This is also called “the grand series.”

Wheel thirds – These are the 12 numbers that are directly situated from across neighbours of Zero. This has a probability of 32.4%, with a payout that is set at 17:1. This is quite like dozen/column bets when it comes to the odd terms and payout.

Zero Game – This is a smaller version of neighbours of Zero. It covers only seven numbers that are closest to slot green zero. There is an 18.9% bet winning odds here, and the payout could be up to 26:1.

The Orphans – The bet that covers the remaining numbers that were not yet mentioned. There is a 21.6% chance of winning this bet, and payouts can be 35:1 or 17:1.

These are fixed call bets. Your variables here are the neighbours where you will place bets on five neighbouring numbers, and your winnings are at 13.5%. The remaining variable is called the ‘finals’ where your bet is on the last digit. Based on the numbers, there is an 8.1% and 10.8% probability.

The European table only contains one zero, and this is a big difference to players. European roulette odds have better odds since there is only one pocket that could make the round fail. That also means there is a smaller house edge in a European roulette compared to American roulette that has 0 and 00.

Some roulette games in Europe have more rules that are more helpful to the player in beating the house edge. If a casino is offering a la partage, that means you are only using half of your even money bet in case the ball lands in zero. The probability of winning a roulette wheel cannot really be predicted because the previous sequences do not impact the current one.

What is the Highest Roulette Odds Probability?

You only have one chance of winning and 37 ways of losing the bet. That means your probabilities in roulette odds are 37 to one, and this makes it a thrill. Calculate odds with roulette odds calculator online.

In order to understand this in terms of money, you must realize that the winner’s payoff is not 36:1 roulette odds because it will be a fair game. It is rather 35:1. The casino will short you out by two units because the casino will not make a profit if it pays odds fairly. Thirty-six will be divided into two and times 100 to reveal a house edge of 5.26%. Hence, roulette odds do not reflect actual roulette payouts. If you check a roulette probability chart, you will see the probability for each set of numbers.

Odds for Success:

–Even, odd, black, red, 1-18, and 19-36 all have a probability of 48.6% if the payout is 1:1.

–1-12, 13-24, and 25-36 have a probability of 32.4% if the payout is 2:1.

–Single number with a payout of 35:1 have a probability of 2.7%.

–Two numbers with a 17:1 payout have a 5.4% probability.

–Three-number combo with an 11:1 payout has an 8.1% probability.

–Four-number combo with an 8:1 payout has a 10.8% probability.

–Six-number combo with a 5:1 payout has a probability of 16.2%.

You can use these statistics when you try the roulette wheel probability calculator, but it does not guarantee anything.

How to Use Probability When Playing Roulette?

You can beat roulette by improving the probability of your odds. Roulette is famous for being a tricky game, and that is because of the huge house edge it has. There is no solution to how you can win roulette each time it spins. However, if you want to maximize your winning potential, you would have to use the odds wisely. Even if it is really based on luck, you can do a couple of things to increase your chances of winning a nice payout.

You must know your odds

The odds that are placed in bets vary greatly, so if you want to maximize your bankroll, you need to know your odds.

If you use a probability roulette wheel in a game, you can find out if you can beat the math in your game.

A system could combine the playing and money management strategy. If you have enough bankroll, you can increase your chance of winning by doubling your bet after each loss, and you will not reach the table limit, which you can easily do. However, this is not really a guarantee.

Whatever your strategy is, they could suffer in the same way. Assuming all wheel numbers have the same probability, which means there is no bias. The math would mean the casino always wins. The system might look great, and it works short term, but if it lands on a number you did not bet on, you are going to lose. The casino will move to winning with a house edge of 2.7% or 5.26%.

There are systems that involve betting on a lot of numbers, like 20. If this is the case, you will win more often because you are betting on most of the numbers. However, if none of them turn up, you will lose all bets. This could wipe out your wins.

What is the Probability of Red in Roulette?

If the ball lands on red, you win 1€. Then, the next step is to bet 1€ on black. Always change the colour when you win. If it’s black, you will lose the first 1€. Then bet 2€ on red. If you lose, you stay in red and double your bet until you win. For instance, losing 1€, you must bet 2€ on red; if you lose again, bet 4€; another loss, bet 8€ on red. When you win, change to black and bet 1€.

If zero comes up, which rarely happens, you lose your 1€. Then, bet 2€ on red again, and keep doing this until you win before you can change colour.

There are 37 numbers on the wheel. There are 18 blacks and 18 reds. Therefore, the winning odds of red are 18/37, which is 0.4865. The odds of black are the same. The same goes for any “even chance” bet that includes highs and lows, and evens and odds. The odds are not changing, no matter how many times red or black have appeared in a row. Consider your loss when you bet on black. What you do not realize is that the odds of red or black coming up is not affected by any sequence. This is the case in all losing roulette online game.

The calculation is very simple. There are no changes except for the amount that you made a bet on. You are either lucky, and you could win back what you lost, or lose it all. The casino owner does not care if you win because they know there is always a loser in every win. If you think about it, there are more losses than wins.

What is the Probability of Black in Roulette?

Since each spin is a new event, black can come up with the same probability as red anytime during the play, no matter how many times each colour wins. Particularly with European roulette where there are 18 blacks, 18 reds, one zero.American roulette has two zeros, which is not good for your winning chances. Hence, the probability of black is 18/37 = 0.4765 or 48.65%.

Black and red have the same probability, which seems paradoxical, and it is expected that the colour changes fast. It could be from a probability point that it is senseless to assume the colour that has not won for a long time could most likely appear now.

American vs. European Roulette

Anyone who is trying to figure out the difference between American and European roulette must understand the double and single zeros, watch roulette rules in 6 min video. The American version has double zeros. In the European roulette, the croupier spins the reel with 37 pockets, and the small ball falls into one when the spinning stops. Any number on the wheel has an odds of 35/1, and if you succeed, you earn your bet back. That means the house edge is 2.7% and the RTP rate is 97.3%

The American roulette wheel is the same, but it has an extra pocket – double zero. The same principle is applicable when you bet on a pocket the ball falls into, and each number has an odds of 35/1. Your stake is given back to you if your bet succeeds. However, even if the odds are the same, your chance of succeeding becomes less because of the extra pocket. Hence, the house edge is 5.26%, and the RTP is 94.74%. Therefore, you have a bigger chance of winning if you play European roulette.

The House Edge Difference

Even if there is only a subtle difference, and it may look irrelevant, it has a huge impact on how your games will turn out.

When there are lower odds, there are bigger payouts. However, as logical as it may be, it is not the same with American roulette. Even if the odds are lower, if you bet on a winning number, you will also get paid 35:1, which is the same in European roulette.

The Return to Player (RTP) Percentage

In roulette, it is essential to take note that this is theoretical because it is based on what is returned to a player on hundreds of spins, and all kinds of bets are available.

You could get great results by just spinning a few lucky spins, or you might not win at all. Players who focus on making Even Money bets such as Black or Red receive more winning bets compared to players who just choose their favourites. However, the odds are only suggesting that.

If you want to consistently win in roulette, you must not base your chances on the sequences and patterns. It is sensible to see 1,2,3 spinning patterns, but that is not different from 31,8,15 spinning. The betting progression does not change except for the amount. You can only beat roulette if you can change the winning odds. You must also take note of the differences between American and European roulette because it can greatly affect your winning chances. Therefore, it is important to know how the Roulette probability calculator works.

Roulette wheel has 37 fields (American one – 38). So, the probability of hitting one of them is 1/37 or 2.7%.

Your winning probability may vary depending on your chosen bet type. If you would decide to pick only one number then you would have 2.7% chance of winning. However, if you would go for a Red/Black bet then you would have a 48.6% chance of winning and so on.

If you would go for Even/Odd, Red/Black or Low/High bets then a probability of hitting is – 48.6%, Column and Dozen bets has a 32.4% probability of winning and a bet on a Single Number has a 2.7% chance of winning.

American roulette has 38 fields instead of 37 (additional 00). As a result, your chances of winning become lower.

Roulette is a game of luck after all and in the end casino will win. Always be aware and gamble only with money you can afford to lose.

Red/Black, Even/Odd and Low/High bets has a highest chance of winning – 48.6%.

A bet on a single number has the lowest chance of winning – 2.7%. However, it has the highest payout – 35 to 1.

By Ion Saliu, Founder of Roulette Mathematical Strategies

I. Mathematics of Winning Roulette Strategy, Systems
II. Glamour and Attraction of Roulette on Gamblers
III. Statistical Analysis of Roulette Spins (Double- Zero)
IV. Free Winning Roulette Systems #1
• Ion Saliu's Paradox and the game of roulette
• Relation of Birthday Paradox to roulette strategies
V. Free Winning Roulette Systems #2
VI. Ion Saliu's Roulette, Gambling Theory, Software Compared to Other Roulette Systems, Strategies
VII. Roulette Links, Resources, Software, Systems

1. The Mathematical Foundation of Winning Roulette Strategy and Systems

The true book of roulette is founded on mathematics, probability theory and statistical analysis of casino roulette spins and random roulette spins. The winning roulette systems, strategies are totally free at this website; the software is free to run with a reasonable membership fee to download.

The common belief in the gambling world is related to the roulette wheel bias. Many kokodrilos (big–time gamblers) swear by the wheel in the sky that they make millions by exploiting the roulette wheel bias. There are plenty of legends. The wheels must have been terribly worn out.

I do have some problems and some remarks regarding the bias of the roulette wheel. I have done the most thorough research in this field. My tool of choice is computer software. My roulette software is not only unique, but founded on solid mathematics. I have analyzed both real–life casino roulette spins and random–generated spins. The reports are very much the same.

Nobody will ever be able to tell which one is the real spin report and which one is the report on computer–generated roulette spins. The number frequencies are the same. I apply a key parameter in my analysis: the SKIP. The skip represents the number of spins between two hits of the same roulette numbers. Again, the skips are the same for both real–life spins and randomly generated roulette spins. The statistical parameters are in accordance to theory of probability. You will see a statistical report on this page, and another one on a different page.

Wheel bias might occur sometimes. It's hard and costly to check very often every roulette wheel in a casino. Later on this page you will see an event of possible wheel bias I witnessed in a real casino. The data sample was not very large, however.

• The second roulette pairing statistical report I told you about is very interesting. If there is roulette wheel bias, then each roulette number must be followed preponderantly by certain numbers. I call this feature number pairing. It is a common feature that occurs in lottery as well. The pairing is also a feature in computer-generated roulette spins. The roulette pairing is not the result of mechanical bias. It is the result of probability theory, IF the results are compatible with the normal probability rule.

I analyzed 1968 real roulette spins recorded at the Hamburg, Germany casino, February 1 – 6, 2000. File name: HAMB00.DAT, component of the BrightR integrated roulette software, systems, utilities.

The results are categorized by the following parameters, in order:
Table or Wheel (Tisch) – Day (Tag) – Month (Monat) – Year (Jahr).

I downloaded the spins at one roulette table or wheel (#1) for the entire month of January 2006. File name: HAMB0106.WH1; 7990 lines (draws or spins) in text format; the last draw of 31 January 2006 is at the very top of the file (line #1). The file contains roulette numbers (spins) only, one number per line. The casino results files have also other data, such as frequency and various statistics. The files also have dashed lines (----) which probably represent dealer changes at that particular roulette table.

HAMB0106.WH1 represents the best recording format for roulette: table by table. Do not mix the spins from different roulette wheels in the same file.

I remarked that same-number repeats are far less frequent than different-number pairing. One roulette number is followed by itself slightly less than once in 1000 spins (on average). But the same number is immediately followed by a different number (best pairing) 3 or 4 times in 1000 spins.

2. The Glamour and Attraction of Roulette on Humans Named Gamblers

I know firsthand how casinos have reacted to my roulette and gambling strategies. They are highly anxious because they can't figure out my systems. Some figured out that I might count losing streaks, or winning streaks, or dealer bust streaks, etc. Of course, I do my best not to let the casinos gain knowledge of my strategies. That's the reason why I do not sell the roulette system unless the customer signs that he/she is not affiliated with a casino whatsoever. It would be illegal for a casino to get their hands on my systems.

Then, I am posed, mockingly, this puzzling fact: Roulette is unbeatable. Great thinkers, such as D'Alembert and Einstein, designed roulette systems that actually fail. I believe Einstein was joking when he presented his infamous roulette system: Always double-up after a loss! What a huge mistake! Like any scientist, Einstein was fascinated with numbers and the unknown, as the roulette game provides. He was, however, very busy with his theory of relativity. He just did not allocate more time to the roulette phenomenon. Otherwise, Einstein's mental programs would have come up with a winning gambling (and roulette) system based, indeed, on the winning/losing streaks. Also, be mindful that Einstein was a religious man. He might as well be the most intelligent mystic who ever lived.

One issue concerns the reaction of casinos to this roulette system and strategy. You may be asked not to use pencil and paper at the roulette table. I stress here that the casinos have NO right to prohibit the use of pencil and paper on the premises. Such an act would represent a form of discrimination. Don't let yourself be intimidated. We all have rights under the law. The courts of law are wide open, including to class action suits.

Finally, I advise against the use of these roulette systems in a cyber casino (online). Internet gambling is prone to very serious fraud. Read the Gambling Odds, House Edge, Integrity, Fraud page for details based on observation and logic. Among other types of fraud: The higher your bet, the higher the probability you will lose it!

3. Statistical Analysis of Roulette Spins (Double-Zero)

The roulette numbers can hit-and-miss in a wild manner. Some numbers can hit frequently in a session (hot numbers). At the other end of the spectrum, some numbers can miss (skip) many spins (roulette sleepers). It is not unusual for a number or two to miss well over 100 consecutive roulette spins!

The FFG median of all skips, however, abides by undeniable mathematical rules (probability formulas). The skip median for single-zero roulette is 25; the skip median for zero-zero roulette is 26.

Many gamblers play roulette strategies based on hot numbers and/or sleeping numbers. I tend to disregard the sleepers by favoring the repeat numbers. You can get acquainted with my roulette strategy founded on the Birthday Paradox in the next section. Axiomatic gambling colleague of mine, you might want to keep a keen eye on that marquee (the casinos should turn it on at every table!)

Beat Roulette With Math Games

4. The Free Winning Roulette System #1

• A diligent, disciplined player can make a weekly profit by COVERING ALL THE NUMBERS BUT FOUR PLAYING NO MORE THAN 10 SPINS A DAY. The four numbers discarded of are the last four spins. You wait patiently, not playing, until the following event occurs. When one of the last four numbers hits again, you get ready to play. You cover all the numbers (0 and 00 including) but the numbers in the last FIVE spins (four numbers to play, because one is a repeat). You place 34 2-unit straight-up bets. Chances are you will win most of the time.
• Next roulette spin, you make the same bet, using now three units per number (you are using some casino money). The first time you won 38-36=2 units; 2 units times 2 = 4 bets profit. The second time: you won 2 units x 3 = 6 units. Total profit per two plays: 10 units. Things are not always like this. Handy Brandy could lose sometimes the first bet. It happens very rarely, but one of the last four roulette numbers will hit again in consecutive sequence.

In most cases, Handy Brandy wins two times in a row without any of the last four roulette numbers repeating. He goes immediately to another table. He knows that the long run 'kills' the casino roulette player more than anything else.

After winning at the second table too, Handy Brandy usually cashes out. He runs out of the casino. Sometimes he might try doing the same things at the third table, but never more than winning at three roulette tables. The player will do the same thing the next day at a different casino and again at another casino... Here is illustrative data from the Hamburg casino. The following figures do NOT represent roulette numbers, but SKIPS. The skips, as in the frequency reports above, represent the number of roulette spins between hits.

9 5 57 17 30 18 0 3 13 25 6 0 4 17 2 24 0 4 3 15 13 8 21 2 23 2 6 7 7 10 3 3 17 10 15 11 1 15 3 1 24 11 10 2 3 13 6 12 3 3 24 6 10 21 4 8 9 8 0 20 7 21 7 18 6 0 17 4 13 5 2 6 16 0 2 4 0 7 0 7 1 8

Beat Roulette With Math Playground

A figure such as 57 represents the skip of a particular roulette number. That particular roulette number (the 3rd most recent in our database) hit after 57 spins. That is, if we look at index 57+3 in our database, we'll find the same number again. Zero in the string above does not represent the 'green 0' (roulette number 0). It means that a particular number hit two spins in row, or hit in two consecutive spins. It couldn't be clearer now.

This page has been written by addition, rather than from the ground up. I added instead of editing and rewriting the material from top to bottom. The page also shows my growing in my linguistic English shoes! It is also clear that a force inside fights me from being too clear! No gambler has ever been more generous with his/her secrets than me!

The casino roulette software program Spins (also SuperRoulette) offers the best graphical representation of this free system. Page-down to the end of the frequency report. The system of interest is named Play all roulette numbers except for the last 5 spins. The report also recommends playing immediately following two consecutive misses (indicated by the – sign).

You only play at the points marked 0 (zero). That's when the last number is a repeat from the previous 5 roulette spins. You will play as above the next 3 points where the skip is zero. In many cases, it's after the third win in a row when you can encounter a string like 0 0. When that happens, you will lose 34 * 2 = 68 units. You improve your chances further when you leave after you won at three roulette tables. You should expect to lose once a week.

Ion Saliu's Paradox and Roulette

Beat Roulette With Math Problems

• If you play 1 roulette number for the next 38 roulette spins, common belief was that you expected to win once. NOT! Only if you play 38 numbers in 1 spin, your chance to hit the winning number is 100%. Here is an interesting table, which includes also the Free Roulette System #1 in the last row.

The maximum gain comes when playing 38 roulette numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as the Free Roulette System #1 scares most roulette gamblers. 'Play 34 or 33 numbers in one shot? I'll have a heart attack!' In reality, the Free Roulette System #1 offers a 28.8% advantage over playing singular numbers in long sessions. In fact, the gain is higher since the bets are placed at optimal moments. That's mathematics, and there is no heart to worry about.

• You can also use SuperFormula to calculate all kinds of probabilities and advantage percentages, including roulette bets. The option L — At least M successes in N trials is a very useful instrument. If you play 19 numbers in one spin, the probability to win is 50%. If you play 19 numbers in 2 consecutive roulette spins, the probability to win at least once is 75%.

Relation of the Birthday Paradox to roulette
The connection between the Birthday Paradox and the game of roulette is extraordinarily appealing to some gamblers. Unfortunately, the appeal has a thin mathematical foundation. The roulette game draws one and only one number at a time. The birthday paradox requires at least two elements. At least two persons in a room..., etc.

If the roulette would draw 10 numbers at a time, the probability would be 72.7% that at least two of the numbers would be equal to one another (i.e. duplicates). But even if the roulette game would consist of 10 spins at a time, the birthday paradox would have nothing to do with predicting the numbers. Some gamblers make the following illogical connection. If I consider 10 roulette spins at a time, in 72.7% of the cases, at least two of the roulette numbers will be repeaters.

So, if I play the last 10 numbers, the chance is very good (almost 3 out of 4 cases) that one of the numbers will repeat next! Wow! That would bankrupt every casino on the planet in a few days! If the roulette strategy would hold true, the probability would rise to 99.8% that the next spin will repeat a number from the last 20 roulette spins! Virtually, play the last 20 numbers and win every time. The cost is 20 units, the payout is 36 units, and therefore that roulette player would make a profit of 16 units in every play!

The cold truth is that the famous and appealing Birthday Paradox merely shows the percentage of sets with duplicate elements in the total elements of an exponential set. That's all. So, unsuspecting roulette enthusiasts do NOT rely on the birthday paradox when playing roulette with real money. If you do, don't ask me for a refund later! Mathematically, it is correct to expect that one of the numbers in the last 26 spins will repeat next with a better than 50-50 chance. It is the median skip calculated by the Fundamental Formula of Gambling. Real life roulette spins and randomly generated roulette numbers validate this law — always.

• I did check, however, several roulette tables in Atlantic City, 2004. I did not find one, not one, roulette marquee showing unique numbers only. Out of 15 numbers, some were repeats — from 3 to 7 repeat numbers. Problem is, the skips between Birthday Paradox situations reached 8+ spins sometimes!
• If I had checked 100 roulette marquees (in Atlantic City), I could have seen four tables showing all-unique roulette numbers! The probability of 15-number roulette strings with repeaters is 96%. Probably some players wait for 5 or 6 or so skips and then apply the Birthday Paradox. The average amount of unique roulette numbers to play is 12. We must win in two spins to make a profit.
• Eventually, I devised a roulette system based onBirthday Paradox formulas, marquee numbers. Apply it intelligently by checking first several tables. Select marquees that show 8+ unique numbers at the top; if not available, start at a roulette table showing the longest string of unique numbers.

The Super Roulette gambling software adds kind of a new system to the Free Roulette System #1. The program adds two more columns to the report. Instead of tracking only the last 5 spins, Roulette tracks also the last 15 spins as displayed on the roulette marquee.

The relation to the Free Roulette System #1. What is the probability that two randomly drawn roulette numbers (spins) will be the same in a group of 5 roulette numbers? It is a Birthday Paradox with 38 birthdays. Instead of 5 persons, we deal with 5 randomly drawn roulette numbers. The probability of at least two collisions (coincidences, or repeats) is: 24%. It's scary for the players of the Free Roulette System #1.

Fortunately, the roulette wheel does not draw 5 numbers at a time. The reports of SPINS show you a more optimistic story. The reports are validated by real-life roulette spins, in a real-life casino. Actually, the analyses of roulette repeats must go much deeper. The roulette probability here refers to chunks of N numbers; e.g. 5 unique roulette numbers versus 5-number groups with at least one repeater...

Months after I published the mathematics of roulette related to the Birthday Paradox, I received negative reports from roulette players around the world. Quite a few casinos decided to turn off the electronic displays (marquees) at the roulette tables. Gamblers say that the decision of casino executives depends on how roulette players stare at the marquees and if the players take notes of the roulette numbers... and especially if they bet big and win big!

I also discovered wide piracy of my mathematical analysis of the Birthday Paradox as a potential roulette system. Even weeks after I published my roulette analysis, there were absolutely no other references on the Internet. Now, there is thousands of roulette systems derived from the Birthday Paradox as I presented it! Beware of other acts of piracy! You can find further information in the roulette resources section of this page.

5. The Free Winning Roulette System #2

The Free Roulette System #2 is presented on Web page: James Bond Roulette System in the Taliban Desert.

By the way, if your bankroll is smaller, you can apply this system in 50-spin sessions.

One more tip. It is possible for a two-dozen (two-column) group to hit more than seven times in a row; or, more than seven out of 10 times. If that happens, you rode a very favorable standard deviation tide. Cash out immediately and move to another table!

My article and the system were provoked by an alleged casino top executive.
'I am currently theChairman of the MGM Grand Casino, and I was advised of this site by way of a memo sent to me.'

In a way, the alleged executive's message is an endorsement of my gambling systems. If the systems were not valid, why bother to risk being rear-end kicked by an understandably angered author? I want to stress again that the casinos have no legal grounds for banning record keeping by the players. Record keeping is also a requirement of tax laws. The rules of private entities do not take precedence over the national laws.

That's how the Free Roulette System #1 came to life as well. I am aware of such tendency now and I believe I have it under control. It will give the player and edge, without a doubt. I have checked for thousands of spins, broken down in 100-spin sessions. There are clearly two situations.

One, the roulette player wins 65 or FEWER spins; it is a losing session. The player counts 100 spins. The player started with 100 chip-units. At the end of the roulette table session, the player counts 61 units. The result was under the standard deviation. Remember to increase the bet the next session.

Two, the player wins 66 or MORE roulette spins; it is a winning session. The player counts 100 spins. The player started with 100 chip-units. At the end of the session, the player counts 69 units. The result was above the standard deviation (calculated for roulette probabilities). Remember to decrease the bet the next session.

The fluctuations in the roulette systems are mathematical, considering the game is totally fair. In an online casino, for instance, the fluctuations go mostly in the favor of the house. The house has to win above the standard deviation — always! Or especially when player's bet is high! That's anything but fairness! This roulette system does not even require strict record keeping. The player can just put aside a chip for each session played, and for each 10-spin roulette groups.

6. Ion Saliu's Roulette, Gambling Theory, Software Compared to Other Roulette Systems

In all honesty, I don't see anything out there that offers better ways to winning at gambling or roulette. I wish there was something easier and more efficient than my approach. Nothing, honestly. IF my casino gambling methodology doesn't win the — there is absolutely nothing to accomplish such daunting tasks. Never will be, if my research has been futile. In the end, it's all about streaks and skips, no matter what the phenomenon is. The skips (misses) are shorter and the streaks are longer if the probability is higher; and vice versa.

The rest of the roulette gambling theory is nothing more than static progression betting and/or clocking the speed of the roulette wheel.

Static progression betting has virtually NO mathematical validity. The number of roulette skips (misses between wins) can be staggering. The winning/losing streaks are dynamic; they flow. It is random, but FFG discerns with various degrees of certainty DC how the streaks move.

Clocking the speed of the roulette wheel is an illusion the myths are made of. NASA sophisticated instruments may be able to measure precisely the speed of the roulette wheel. But NO instrument can predict the landing position of the spinning ball on the roulette wheel. The wheel deflectors randomize the movement regardless of the speed. Of course, it is absolutely impossible for any roulette player to clock the roulette wheel speed precisely, even if the casinos allowed the use of any instruments or computers on the premises.

Not to mention the thorough tests conducted by the manufacturers of roulette wheels. They certainly perform tests regarding the wheel speed and the landing of the spinning roulette ball. They probably run the roulette wheel at exactly the speed v (rotations per minute) for a number of runs R. They note that the roulette ball is landing randomly; i.e. in various positions on the wheel. They change the wheel speed and run another batch of tests. They notice the randomness of the ball landing. It is a strong fact regarding the roulette wheel. The same speed of the roulette wheel leads to highly random landing positions (roulette numbers).

I did notice bias, however. It was due to the wear of the roulette wheel. Probably the deflectors of the roulette wheel were worn out. The wheel was malfunctioning, anyhow, I think. We can divide the roulette wheel in two sections based on the last number drawn. There are 38 numbers in double-zero roulette. The last number drawn, plus 9 numbers to its left on the roulette wheel layout, plus 9 numbers to the right on the layout = make up the inside hemisphere of the roulette wheel. The other 19 numbers make-up the outer hemisphere.

The next number should be FFG-equally distributed between the two wheel hemispheres. That is, the roulette insiders and roulette outsiders should be FFG-equally distributed. I tracked the spins at a roulette table in Atlantic City. To my (belated) dismay, the ratio was 80% to 20% biased towards the outer hemisphere! Actually, two roulette dealers — a woman and a man — shifted at the table during that continuous run! So, it was not a so-called roulette dealer's signature! It was a malfunctioning of the roulette wheel.

It is likely that the casinos have no knowledge of such phenomenon. But tracking the landing in the roulette inner hemisphere and the outer hemisphere is pretty hard to accomplish when actually playing roulette in a casino.

Later on, I decided to release special roulette software that works with the roulette wheel sectors and the Birthday Paradox. Program name: RouletteHemis; software category 5.5.

Right now, I cannot see any casino roulette gambling system better than mine. That's the only way, like my gambling theory and software do: Track the winning and the losing streaks and their corresponding skips (misses). Apply the Fundamental Formula of Gambling (FFG). There will be some no playing moments (or play the minimum bet); other situations demand a higher roulette bet. It is hard work, but nothing else works better. It might not be attractive to the faint at heart or the illusion-drinker.

Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on valuable mathematical discoveries with a wide range of scientific applications, including probability theory applied to roulette gambling, software, real winning systems.

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