Best European Roulette Strategy

Introduction

The Gambler's Fallacy is the mistaken belief that if an independent event has not happened in a long time, then it becomes overdue and more likely. It is also equally incorrect that if an outcome has happened a disproportionate number of times lately, compared to statistical expectations, then it becomes overheated and less likely to occur the next time. An example of this fallacious thinking might be that if the number 23 hasn't been drawn in a 6-49 lottery the last 100 games, then it becomes more likely to be drawn during the next drawing.

Many worthless betting strategies and systems are based on belief in the Gambler's Fallacy. I got the idea for writing about this after reading an 888 online roulette article by Frank Scoblete entitled How to Take Advantage of Roulette Hot Spots. In that article, Scoblete recommends taking a count of each outcome for 3,700 spins in single-zero roulette and 3,800 spins in double-zero roulette in the hunt for 'hot numbers.' Never mind that this would take about 100 hours to make this many observations, assuming the industry standard of 38 spins per hour.

Before going further, let me say that I strongly believe modern roulette wheels made by top brands like Cammegh are extremely precise and any bias would be minuscule compared to the house advantage. Thus, testing a modern roulette for bias would be a total waste of time. Now, testing a 30-year-old hand-me-down wheel in a banana republic might be another story. However, you're on your own if you win a lot of money from said casino and try to leave with it.

That said, if you track 3,800 outcomes in single-zero roulette, the average number of times any number will hit is 3800/38=100. I ran a simulation of over 1.3 trillion spins, counting how many times each number was hit, sorting the outcomes to find the most frequent number and how many times it was observed, and keeping a count of how many times the most frequent number in each simulation was seen.

Hottest Number in 3,800 Spins of Double-Zero Roulette

The Constant Bet roulette strategy is not very advanced. This is the 'strategy' used by a majority of roulette players, often without even realizing it. As its name suggests, this strategy is about constantly placing the same bet. It also involves continuously betting a constant amount of money. Roulette is commonly referred to one of the most thrilling casino games. As exciting as roulette may be, the odds are not the most favorable at the casino. French Roulette has the highest payout percentage of 98.65 percent, followed by European Roulette at 97.30 percent and American Roulette at 94.74 percent. Much of roulette play is based on. Best Roulette Strategy for Optimal Results. There are three main types of Roulette game available, and each one has its differences from the others. As you can see, in the example we have 7 losses and only 3 wins – but we managed to come out at a profit. It might seem really similar to the Martingale strategy, but consider this – if we were on a 4-round losing streak while using Martingale, we would be at a loss of £31, and if we won the fifth game, we would have made a profit of only £1.

As a former actuary, I hate to use a layman's term like the 'hottest number,' but that is how gamblers talk so will go with that. That said, following are the results of the count of the hottest number in millions of 3800-spin simulations.

Count of the Hottest Number in 3,800 Spins on Double-Zero Wheel

Here is what the table above means in plain simple English.

• The mean, or average, count of the hottest number is 122.02.
• The median count of the most frequent number is 121. This means that over 50% of time the most frequent number appeared 121 times or less, as well as 121 times or more. This is possible because the probability of 121 observations is in both groups.
• The mode, or most count of the hottest number is 120, which happens 8.29% of the time.
• The 90th percentile is the smallest number such that the probability the count of the hottest number is at least 90% .
• The 95th percentile is the smallest number such that the probability the count of the hottest number is at least 95%.
• The 99th percentile is the smallest number such that the probability the count of the hottest number is at least 99%.
• The 99.9th percentile is the smallest number such that the probability the count of the hottest number is at least 99.9%.

Hottest Number in 3,700 Spins of Single-Zero Roulette

The results are very similar with 3,700 spins tracked on a single-zero wheel. Following is a summary of the results.

Count of the Hottest Number in 3,700 Spins on Single-Zero Wheel

The following table shows the full results of the simulation on both wheels. The two commulative columns show the probability that the count of the hottest number is the number on the left column or more. For example, the probability the hottest number in 3,700 spins of single-zero roulette is 130 or more is 0.072044.

Summary of the Count of the Hottest Number in 3,700 Spins of Single-Zero Roulette and 3,800 spins of Double-Zero Roulette

Count of the Hottest Numbers in 300 Spins in Double-Zero Roulette

What if you don't want to spend 100 hours gathering data on a single wheel? Some casinos are kind enough to give you, on a silver platter, the number of times in the last 300 spins the four 'hottest' and 'coolest' numbers occurred. The image at the top of the page shows an example taken on a double-zero wheel at the Venetian.

In 300 spins, the average number of wins on a double-zero wheel for any number is 300/38=7.9. As you can see from the image above, the four hottest numbers were 20, 5, 29, and 2, which occurred 15, 14, 13, and 12 times respectively. Is this unusual? No. In a simulation of over 80 billion spins, the most frequent number, in 300-spin experiments, appeared most frequently at 14 times with a probability of 27.4%. The most likely total of the second, third, and fourth most frequent numbers was 13, 12, and 12 times respectively, with probabilities of 37.9%, 46.5%, and 45.8%. So the results of the 'hottest' numbers in the image above were a little more flat than average.

The following table shows the probabilities of the four hottest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.009210.

Count of the Hottest Four Numbers in 300 Spins on a Double-Zero Wheel

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

Best European Roulette Strategy Game

Summary of the Count of the Four Most Frequent Numbers in 300 Spins of Double-Zero Wheel

Count of the Coolest Numbers in 300 Spins in Double-Zero Roulette

The next table shows the probability of each count of the four collest numbers in 300 spins of double-zero roulette.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of double-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Double-Zero Wheel

Count of the Hottest Numbers in 300 Spins of Single-Zero Roulette

In 300 spins, the average number of wins on a single-zero wheel for any number is 300/37=8.11. The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.015727.

Count of the Hottest Four Numbers in 300 Spins on a Single-Zero Wheel

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

Summary — Count of the Four Hottest Numbers — Double-Zero Wheel

Count of the Coolest Numbers in 300 Spins in Single-Zero Roulette

The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third coolest numbers will be observed five times is 0.287435.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of single-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Single-Zero Wheel

The least I hope you have learned from this article is it is to be expected that certain numbers will come up more than others. To put it in other words, it is natural that some numbers will be 'hot' and some 'cool.' In fact, such differences from the mean are highly predictable. Unfortunately, for roulette players, we don't know which numbers will be 'hot,' just that some of them almost certainly will be. I would also like to emphasize, contrary to the Gambler's Fallacy, that on a fair roulette wheel that every number is equally likely every spin and it makes no difference what has happened in the past.

Finally, it should not be interpreted that we give an endorsement to the 888 Casino, which we linked to earlier. I am very bothered by this rule in their rule 6.2.B. Before getting to that, let me preface with a quote from rule 6.1, which I'm fine with.

'If we reasonably determine that you are engaging in or have engaged in fraudulent or unlawful activity or conducted any prohibited transaction (including money laundering) under the laws of any jurisdiction that applies to you (examples of which are set out at section 6.2 below), any such act will be considered as a material breach of this User Agreement by you. In such case we may close your account and terminate the User Agreement in accordance with section 14 below and we are under no obligation to refund to you any deposits, winnings or funds in your account.' -- Rule 6.1

Let's go further now:

The following are some examples of 'fraudulent or unlawful activity' -- Rule 6.2

Next, here is one of many examples listed as rule 6.2.B

'Unfair Betting Techniques: Utilising any recognised betting techniques to circumvent the standard house edge in our games, which includes but is not limited to martingale betting strategies, card counting as well as low risk betting in roulette such as betting on red/black in equal amounts.' -- Rule 6.2.B

Let me make it perfectly clear that all betting systems, including the Martingale, not only can't circumvent the house edge, they can't even dent it. It is very mathematically ignorant on the part of the casino to fear any betting system. Why would any player trust this casino when the casino can seize all their money under the reason that the player was using a betting system? Any form of betting could be called a betting system, including flat betting. Casino 888 normally has a pretty good reputation, so I'm surprised they would lower themselves to this kind of rogue rule.

Written by: Michael Shackleford

Roulette is one of the most popular table games in modern casinos. Although variations on the game have been around for several hundred years, there are now only 3 variations in American casinos.

You’re likely already familiar with American roulette and European roulette. The most recent addition to the table game inventory is Sands Roulette.

Which of these games should you play?

How should you bet on them?

What’s the smartest strategy for roulette betting?

I’ll explain all that in this post:

What Are the Differences between American, European, and Sands Roulette?

Although these games have a few other differences, the most significant distinction between the 3 versions of roulette are the number of green slots the wheels contain.

Every roulette wheel has at least 37 slots.

36 of those slots are always numbered 1 to 36, and they’re alternately colored RED or BLACK.

The additional slots are green.

In European roulette there is only one green slot, the “0”.

In American roulette there are two green slots: “0” and “00”.

In Sands roulette a third green slot, “S”, has been added to the wheel.

The green slots are there for one reason:

They make the game’s statistical probabilities uneven.

This is because of the way roulette bets are paid off. You can win anywhere from 35-to-1 (for betting on a single number) down to 1-to-1 (for betting on 18 slots at a time).

The payoffs, called “odds”, are not as fair to you as the actual estimated probabilities of the roulette ball landing on any given slot. This is how the casino makes its money.

In a game of roulette the house should keep at least 2.70% of all the bets players make over time. The casino has no need to cheat the players. In fact, the players often make really bad bets that improve the “house edge”, as that casino profit is called.

One of the other differences between European roulette and both American and Sands roulette is that the European roulette table has an additional betting area. This secondary betting area is used to place specially designed bets. They are more complicated than the normal bets made in American and Sands roulette. I’m going to ignore this section of the table, because I’m going to show you how to place bets that have the best chances of paying off.

Is There a Winning System for Roulette?

Everyone who gets into roulette sooner or later starts to think about how they can “beat the system”.

I’m going to be honest here:

There is no way to do that.

The green slots on the wheel make it impossible for anyone, anywhere, to ever design a betting system that is guaranteed to win. If you really want to guarantee yourself a win every time, then put a chip on each of the 2-to-1 outside bets and on each of the green number bets.

That’s the only way you’ll be paid money every time the wheel spins.

You’ll also go broke.

You may have heard about a system called the Martingale System. It’s a popular betting system with new roulette players.

Experienced roulette players just turn their heads and roll their eyes when someone mentions the Martingale System. The only way you can make money with the Martingale System is to write a book about it and get people to buy your book.

Even that’s a gamble, though, because most people now know that the Martingale System promises more than it delivers.

Here’s how this system works:

You start out betting the minimum. If you lose, you double your bet. If you win on your doubled bet, you go back to betting the table minimum. If you lose again, you double the size of your bet again.

This sounds great to inexperienced bettors but the problem is that you’ll either run out of money or hit the table limit before you can recoup your losses as they add up.

The Martingale System is a sucker bet, plain and simple.

Every betting system in every form of gambling tries to leverage probability theory. The Martingale System and other roulette betting strategies also rely on probability estimates.

But there’s a flaw in the thinking behind these systems. If you account for the flaw you’ll be okay. You won’t always win but your expectations will be more reasonable.

The secret to not going broke when you gamble is to set reasonable expectations and maintain your self-discipline. You should never drink or take drugs when you gamble. They lower your inhibitions and impair your judgment.

You might as well just hand your money over to the casino at the cashier window and say “keep it” if you’re going to drink or do drugs when you gamble.

How Do Probabilities Work in Roulette?

Probability theory came out of statistics. It tries to give us rules by which to guess what happens next in any situation. The guesses are seldom accurate predictions. Sometimes the guesses work out, and sometimes they don’t. Gamblers love probability theory because they think it helps them pick the best betting strategies.

You’re actually more likely to double your money during a roulette session if you put all your money on a single bet. The more bets you place, the less likely it becomes to double your money.

That’s because every bet brings you close to the long term expectations. The closer you are to the short term, the more likely you are to get better than expected results.

In roulette, the probabilities are simple. The dealer spins the wheel and releases a ball that whirls around the outside of the wheel and finally settles in a slot. With only 37 slots on a European roulette wheel you have a 1-in-37 probability of the ball landing on a specific slot.

This probability never changes.

This probability is calculated on the basis of all the known possibilities.

What probability theory cannot do, however, is predict where the ball will stop.

Nor can it predict whether the ball will land on red, black, or green any number of times over the next 100 spins.

Nonetheless, a lot of gambling guides tell you that you have the best chances of winning if you do this because of such-and-such probabilities. And many of these guides warn you that there is no way to predict the future, but by setting the expectation that the ball will land on red about 47% of the time, these guides are making predictions and promises they cannot keep.

They’ll even back up their claims by talking about how to run computer simulations for 1 million spins of the wheel so that you see how often the ball lands on red, black, or green.

In the real world the Probability Fairy is always on vacation. She’ll never be there to wave her magic wand to make things happen the way experts say they should. The ball could land on red over the next 20 spins. Or it could land on black or green or some random mix of color combinations.

You have no way of knowing how many of the next [X] spins will turn out a certain way. Talking about probabilities in this way is just dishonest.

What you can do is look at the wheel and ask yourself how much it costs to bet on the largest possible set of numbers. The idea here is to get as much coverage as you can without losing money too fast.

But even if you cover every number on the wheel you’ll lose money.

So the only way to win in roulette–and this is completely random, never guaranteed–is to bet on less than all the numbers on the wheel.

You also want to play bets that pay better than even money. You can place a variety of bets, but most of them aren’t worthwhile.

Betting on single numbers is a bad idea. You can place bets on the lines between the numbers (these are called “street bets”) and on lines at the corners of numbers (these are called “corner bets”).

But even though you get pretty good odds (payoff) you’re still covering too few numbers.

How Bets Work in Roulette

Divide the bets into two groups:

1. Inside bets
2. Outside bets

Inside bets are based on individual numbers or small groups of numbers. When you see players betting on the lines, corners, and individual numbers on the table they are making inside bets.

Outside bets are based on pre-selected groups of numbers on the wheel. The “2-to-1” bets cover 12 numbers each: 1 to 12, 13 to 24, and 25 to 36. The “1-to-1” or “even money” bets cover 18 numbers each:

• Odd
• Even
• Black
• Red
• 1 to 18
• 19 to 36

Best European Roulette Strategy Games Pc

The bets more likely to pay are the even money bets.

But unless you can win 5 times out of 9 on even money bets you’ll lose your stake. That’s the problem with roulette. You always have to win at least 1 more time than you lose no matter how you place your bets.

The “2 to 1” bets pay better than the “1 to 1” bets because they cover fewer numbers. You have less of a chance of winning.

There are 6 types of “2 to 1” bets:

• 3 kinds of dozens bets: (1 to 12, 13 to 24, and 25 to 36)
• 3 kinds of columns bets: ([1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34], [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35], [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36]).

You can make a bet by betting on any two of the “2 to 1” groups. That means that instead of covering only 18 numbers you’ll be covering 24 numbers.

This type of bet is often called the “double dozen” bet. It’s popular among gamblers who like to hedge their bets. They have a better chance (all other things considered) of scoring a win with a “double dozen” than with one of the standard even money bets. If you’re playing it safe and going for even money odds, you should always play a double dozen bet.

If you want to bet more aggressively, then instead of betting more money on your double dozen, you can cover all 36 of the red and black numbers. Leave the green numbers alone. Yes, they’ll come in every now and then, and you’ll lose money.

But there’s a way to keep your losses low.

How to Bet on Columns or Dozens Aggressively

Take 6 chips and distribute them across EITHER the three dozen bets or the three column bets.

Place 3 chips on 1, 2 chips on the 2nd, and 1 chip on the 3rd. If the ball lands on a green number you’ll lose your entire bet, so always play the table minimum with this aggressive style.

If the ball lands on any number with your single chip bet, you’ll win 2 chips and lose 5–for a net loss of 3 chips (half your bet).

That’s the safest way to bet aggressively on the table.

If the ball lands on any number in your 2 chip bet you’ll win 4 chips and lose 4 for no loss. This keeps you in the game.

If the ball lands on any number in your 3chip bet, you’ll win 6 chips and lose 3 for a net gain of 3 chips. This will offset 1 single chip win.

The way this betting strategy works out, your money can grow substantially and still take some big hits. Where the strategy will fail you is when the ball lands on green or if the ball lands on the single chip bet more often than it lands on the 3 chip bet.

Sorry, but there’s no way to prevent that from happening.

There Is No Guaranteed Way to Win in Roulette

I can’t say this often enough:

You can’t win at roulette in the long run.

I think roulette is a fun game to play. It’s exciting because you don’t know where the ball will land. You take an active role in making your wagers.

And you’ll find there are a lot of different betting systems to experiment with. The only thing that is guaranteed in roulette is that the casino will make a profit. What you hope for is that they make their profit at someone else’s expense.

Players who try to improve their luck by making big bets do sometimes win, but most often the people who come out ahead are the patient players who use conservative betting strategies and take money off the table. If you only walk away with your beginning stake you’ll be luckier than most gamblers.

And you can take that to the bank.