The rules for roulette tables are designed in such a way that the bank makes money in the long run. It may be a hard truth, but the reality is **there is no system to beat the roulette wheel**.

Nevertheless, it must be said that roulette is a pretty fair game. If you play with only small amounts (relative to your chips), then you can gamble for a long time at the roulette table whilst having a lot of fun.

This article shows you how to calculate probabilities in roulette, including the odds for each type of bet, allowing you to analyse all the possible variations.

Collage of Shutterstock images;

Foreground: donskarpo,

Background: Nata789

Foreground: donskarpo,

Background: Nata789

The calculation of roulette wheel probabilities is very simple.

Let us take the classic example of a dice with the numbers one to six. How large is the probability that the next throw is the number five?

Of course, it is **1/6** or **16.67%**: only one side of the dice has the number five, one of six numbers in total.

And how big is the probability of getting a number that is *at least* four?

The answer is **50%**: there are three possible throws (numbers four, five and six), meaning a three in six chance, or **1/2**.

If you have understood these simple examples then you will also be able to understand the probabilities expected in roulette.

Roulette has a total of **36** numbers, one to 36. The 36 numbers are divided into the following equal sized ‘sets’:

- 18 red numbers (Rouge) and 18 black (Noir)
- 18 even numbers (Pair) and 18 odd (Impair)
- 18 numbers in the lower half (Manque) and 18 in the higher half (Passe)

Lastly, there is an additional stand-alone number, which is the green “zero”, making 37 numbered zones in total. The zero is not included in any of the three sets above.

So, if you are gambling on any of the three sets, in other words;

- red or black
- odd or even
- low or high

then your likelihood to win is **18/37** = **48.65%**. If your bet wins, your stake is returned plus 100%. In effect you double your money as each of these sets is an ‘evens’ bet.

Assuming the frequency of results is uniform (i.e. each number appears once during every 37 rotations), the bank will win all bets placed on the three sets every 37th round, when the green zero arrives. Thus, players lose an average of 1/37 of their stakes (assuming that they always play with the same stake per round).

Putting this another way, imagine you are betting on both the “red” and “black” sets at the same time. On average, 36 out of 37 times, the roulette ball will land on a number from one to 36. You are backing all 36 numbers and will lose one bet each time but receive full compensation on the other. (A zero sum game). But you will make a total loss (lose both bets) when the ball lands on zero, and this is precisely the case in 1/37 of the games.

So you can say that with simple chance you should expect returns of 36/37 of your stake money, which is the expected value in roulette (**97.3%**). In other words, for every 100 units staked you will receive back an average of only 97.3 units.

There are some casinos which are a little fairer to players who rely on simple chance. In such a casino when betting on, for example, red, if a zero appears your stake is not lost immediately but is left to ride on the next spin of the wheel.

In this case, the stake is returned to you (without winnings) if the next spin is “red”. The expectancy value for this type of house increases a gambler’s chances to **98.65%**, or 98.65 units returned per 100 unit stake. Wagering with 100 units in a session will cost an average of 1.35 units (the house “edge”). You’ll find further maths and explanations in Wikipedia **here**.

If you witness “red” five times in a row, what do you think should come next? Red or black?

Many will believe that the chances for “black” are now higher. Black has not appeared for a while so it must surely arrive again soon to ‘balance out the frequency’.

Unfortunately, this thinking is incorrect. Following a series of “red” five times in a row, the probability for black always remains the same: 18/37 = 48.65%. Just remember the roulette wheel has no memory – it simply does not know what the last number was.

This is why it makes no sense to write down the sequence of red and black. (Surely you must have observed gamblers in casinos engaging in this habit?). It is impossible to detect even the smallest patterns in the roulette wheel because the ball has no memory and will always churn out numbers completely at random.

However, it is *unlikely* that “red” will appear six time in a row. The chance of six reds in a row is

(18/37) ^ 6 = **1.3%** (i.e. 48.65% x 48.65% x 48.65% x 48.65% x 48.65% x 48.65%). *(For more explanations see also our combinatorics article)*. By the way, this is approximately half the chance that any one single number appears (1/37 = 2.7%) and, of course, it is just as unlikely that there will be red numbers five times in a row followed by a black number; the probability for this sequence is also

To give you a better feel for roulette probabilities, here are a few examples. Here we use “r” for red and “b” for black:

- r or b: 18/37 =
**48.65%** - rr or bb: 18/37 x 18/37 =
**24%**(two reds in a row or two blacks in a row) - rb or br: 36/37 x 18/37 =
**47.3%**(one colour followed by the other) - rrr or bbb: 18/37 x 18/37 x 18/37 =
**11.5%** - rbr or brb: 18/37 x 18/37 x 18/37 =
**11.5%** - rrrr or bbbb: 18/37 x 18/37 x 18/37 x 18/37 =
**5.6%**

Never confuse these probabilities with the “conditional probabilities”. The chance of red four times in a row is **5.6%** but if you come to the table immediately after a red number has appeared, the probability that you will witness a further three reds (making a total of four times in a row) is **11.5%** – purely because you will be observing only a series of three rounds.

The law of small numbers was first conceived in 1898 by **Ladislaus Bortkiewicz** (1868-1931). His book is still available in German, free of copyright, and can be downloaded as a **PDF or Kindle** version. An **English language introductory text** is also available.

The Law of Small Numbers is not exactly bedtime reading material, but here is a brief summary. As roulette is a game of repetitions the “law of a third” and the “law of two-thirds” should become evident as play continues.

If there are exactly 37 rotations performed at roulette (as many as there are different numbers), according to the book:

- approximately one third of the numbers (around 12-15 numbers), will
*not be hit at all* - approximately one third of the numbers will appear
*exactly once* - approximately one third of the numbers will appear
*twice or more* - approximately two thirds of the numbers will appear
*at least once*

The law of large numbers states that with an increase of repetitions the actual observed frequency comes closer to the theoretically calculated probabilities.

Although it is possible to observe on one particular evening, for example, red numbers coming up 60 times in a row, and another evening 40 times black, ultimately, when you observe the distribution of red and black over a longer period, the frequency will be closer to 50:50.

Therefore, **there is no roulette system with which you can beat the probabilities**. It may seem for a short time that a certain system functions but, in the long run, you will lose money with every system because roulette rules are designed in a way that the casino earns money. Period. Bear this in mind when you play roulette, but it is still fun!

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In the 1960’s the US mathematician Edward O. Thorp published a ground-breaking book entitled ‘**Beat the Dealer**’, which ultimately earned him the nickname of ‘the father of card counting’. In his book he revealed a revolutionary point scoring system that has since been successfully used by professional and amateur card players for more than two generations.

Counting systems have since been further developed and there is now a plethora of more or less similar techniques, some more complex than others, but in the end all giving the gambler an advantage over the house.

** Card Counting is actually pretty simple maths.** The only real skill necessary is to be able to add-up and count in your head like a machine gun. Not everyone can do it, but it goes without saying that the less effort you need to make on the counting, the more concentrated you can become on appearing as just another ‘normal’ player at the table.

One of the most profitable and perhaps the easiest way to count cards is known as the Hi-Lo strategy (allocating high and low cards in the game a value). This system is basically a ‘Running Count’ technique in which each card has a certain value.

The system is used to identify when the ratio of cards already played with high value is unbalanced compared to cards with low value.

Cards such as Tens, Picture Cards and Aces, not only increase the chance that a Blackjack is due, but also increase the chance of future hands which are worth at least 20.

A deck which includes many high cards brings the player into a very profitable situation, because it increases the chance that the dealer loses.

In a situation where the majority of cards left in the shoe have a value between 2 and 6, the dealer has a significant advantage over the player.

The more high cards left in the deck to be played, the higher the chance that the dealer loses.

From the moment the first card of a new mixed deck is dealt, the player begins to count the card values (+1, 0, -1).

A low card (2, 3, 4, 5, 6) increases the count by one point, a high card (10, J, Q, K, A) decreases the count by one point. This is called the ‘running count’.

The cards 7-9 are neutral and are not counted in the Hi-Lo system.

So, your count may look like this in any round:

Count the total number for this round, and you should come up with +1.

This count means that more cards with a low value have already been played, meaning there are more high value cards in the remaining deck (10, J, Q, K, A). However, you need to keep in mind that the count cannot be very accurate after just a few hands. It is important to collect more information for better accuracy and greater advantage over the house.

If you are trying Blackjack card counting for the first time, you can just flip through a whole set of cards. If you count correctly then you will end up with a ‘0’ at the end of this exercise.

The first few times may be trial and error, but the more you practice, the faster and more accurate you will become. After a while you can try to count two cards at once, just by looking at the hands. If you practice long enough then you will almost automatically recognize various card combinations and their value. And that’s the great thing about this simple Hi-Lo strategy. It’s very straightforward and easy.

It will not be long before you can apply this simple technique and at the same time play blackjack at normal speed. You need to keep the current value in mind and at the same time focus on the game without drawing attention to yourself.

If you have not yet mastered the counting system by heart and need to think long until you get to the current value, then you will stand out to the dealers and security staff because they are trained to detect counting behaviour.

After you have mastered the counting itself, the next step is to know when it’s worthwhile to start staking and how much to bet. As already mentioned, the rule of thumb is that the closer the table is to the end of the deck, the more predictable the outcome.

Here, a new factor comes into play known as ‘True Count’. Divide the running count by the estimated number of remaining decks in the card shoe. This is the part that beginners get confused with.

Let’s look at an example.

The running count is +7 and there are about 4 decks left. The true count would be 7/4 = 1.75. Round that up to 2, keep it simple.

Converting the Running Count into the True Count is about getting a more accurate estimation of whether or not you have an advantage.

These days you won’t find many single deck games, so it’s likely that you will be playing on a multiple deck table. These can range from two to eight decks so you will have to estimate the number of remaining decks.

One way of determining how many cards have already been dealt is to look at the discard tray on the table (if there is one). Practice estimating at home by piling decks of cards on top of each other.

Once you have estimated how many decks have been played you then need to subtract this number from the number of decks the game started with. This is the number of decks remaining.

Here is an example for a six deck game.

You have a running count of 12. You look at the discard tray and see that approximately three decks have been played meaning that there must be still three decks remaining. You divide the running count of 12 by 3 to get a true count of 4.

Now it gets interesting…

This is where card counting becomes more art than science. Some blackjack books give rigid rules on how this should be done. However, casino employees are also aware of the published techniques and certain betting patterns can easily betray a card counter.

The key to making money as a card counter is raising your bets when the deck is ‘hot’, and lowering them when the deck is ‘cold’. The variation in size is known as the ‘Betting Spread’. The range of an individual’s betting spread depends on a lot of personal factors such as bank size, comfort level, proficiency in card counting, knowing the rules, etc.

However, in order to avoid undue attention from casino staff a bet spread between 1 and 5 units is recommended. This means that you should bet 1 unit for a +1 count, all neutral counts, and all negative counts. A +2 count means 2 units staked, a +3 count means 3 units, a +4 count means 4 units. Anything over +4 signifies a bet of 5 units. Exceeding 5 units is likely to attract unwanted attention from the casino hierarchy.

The size of the individual unit depends on your preferences. To stay under the radar you should identify a range between table minimum and maximum.

Table Minimum: £5

Table Maximum: £200

The player must estimate the top end of the count. In other words, how high may the count get in that session? For simplification, we estimate the maximum count at 10. This means that the top end of the player’s personal range is £100, a multiple of £10.

Your Personal Maximum: £100

Count if at 0 – Bet £10

Count is at 1 – Bet £20

Count is at 2 – Bet £30

Count is at 4 – Bet £40

And so on…

Of course, it becomes even more interesting if the table is only approached when the deck is ‘hot’, but this requires a team of card counters.

This may sound unreal, but anyone who has seen the film ‘21’ (2008), has watched a good, entertaining movie and also witnessed that a team strategy can be successful.

With card counting it is actually possible to gain a decisive advantage over the casino. Many have tried and with great success!

Casinos are not stupid. Although card counting is not legally prohibited or punishable, neither under German law, nor in the US, it does not mean that casinos turn a blind eye to card counters.

Some of the more common countermeasures include:

- The number of card packs used in a shoe is increased. Initially Blackjack was played with just one deck, later with four, and now mostly with six decks
- The shoe is never played to exhaustion. After a quarter or a third of cards are played there is a ‘cut off’ and the shoe is reshuffled.
- The player’s staking choices are limited, for example:

(a) Double down is only permitted on hard totals of 9, 10, or 11

(b) No doubling allowed after splitting two cards of the same denomination

The above countermeasures certainly increase the house edge, but card counting players are still able to play winning systems in spite of them.

Therefore, many European casinos now use ‘Shuffle Stars’, which are special card shoes. Played cards are immediately mixed back in with the other cards making each round independent of the next, like in roulette. Hence, card counting has become not only difficult but a thing of the past in most casinos today.

We hope that this article about blackjack and card counting has enlightened you. Once you think that you are ready it’s time to try, but serious playing is not just going to the next best Internet casino but to the best one. But which one is the best?

Check **Bestonlinecasino.uk **. What distinguishes them from others is that when they say 888 Casino is the top choice for UK players, they actually have the stats to prove it!

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Because if they are, success with online gambling boils down to the statistics and probabilities of the game, which should be calculable in order to forecast potential earnings.

In this article we will talk about gambling in the sense of a “luck based game”, whilst remembering how some games might be beaten whilst others cannot.

In a nutshell, if online casinos are fair, then there is a chance of profiting from them.

Firstly, let’s have a look at what most online casinos offer. Whether new or old, most offer traditional casino games like poker or blackjack, but many of the newer casinos concentrate on providing online versions of “slot machines”.

These usually play in any browser or with apps on your phone or tablet. The principle remains as easy to comprehend as the multitude of digital slot machines you find in public places: Watch a few reels spin, and win depending on the final symbols displayed.

Online, many new casinos try to attract customers with free spins on their flagship games. You may already have been exposed to such ads from sources such as Facebook users who claim to have won thousands of pounds with these trial spins.

An initial step towards answering whether online casinos such as these are fair or rigged is this:

Even if the probabilities are calculated fairly and regularly, **the “free” spins are usually not free**.

For example, you only receive your allotted free spins after paying for a separate number of spins. Or, you only receive your winnings if you also make the same amount with regular betting on the site’s sportsbook.

These little tricks are designed to lure new gamblers and ensure that they invest more than they get “for free”.

You can find online casinos everywhere on the Internet. New ones appear all the time and, as mentioned, many offer bonus payments, free spins, or other forms of “welcome packages”.

When judging how trustworthy online casinos are, you should of course use your common sense:

Websites with strange marketing strategies should be avoided, offers that seem “too good to be true” are not true, and anyone asking for your payment information to give you a “free present” does not want to give you a free present.

Here’s a list of five criteria to judge when deciding on the legitimacy of online casinos in the UK:

- Are they licensed by the Gambling Commission? Any provider of online gambling services such as poker, slot machines or even bingo needs to have a licence to offer gambling legally in the UK. This licence is essential and no gambling provider who has it would make you search for it. If you cannot find it, it’s probably not there.
- If you really want to make sure, look them up in the Gambling Commission’s official list of licensees – this won’t take long.
- Find out the experiences of others with this online casino: Can you google the site and get an impression? If everything is great and no-one ever complains then this may trigger alarm bells. And finding only negative reviews about a site is more than dubious.
- At least scan the terms & conditions for certain areas or keywords: Do you have to sign up for a certain period of time? What fees do you have to pay from your winnings?
- Review the payment methods. Many online casinos offer PayPal apart from credit cards. This can help you control how much you are investing.

Online casinos that pass these simple tests are usually trustworthy.

Note that while there are certain regulations for gambling machines, for example, that there has to be a chance to win the jackpot in every single game, there is no rule restricting the odds for any games.

The usual physical restrictions also do not apply. For example, you cannot card-count since there are no physical cards and no deck to draw from.

While online casinos adhering to the rules are legit, they are not necessarily “fair” in the sense you might understand the term.

One golden rule of gambling is that the bank always has an advantage. They have to, otherwise they could hardly maintain expensive casinos in “real life”, or the cost of their server online.

From a mathematical point of view what you can get from online casinos might be fun or excitement if you are the type to get excited about bets, but you cannot expect profits from virtual slot machines.

These have to be the ultimate test in patience and endurance, clicking a button hundreds of times in the hope that a random number generator might declare this round the jackpot.

Simple games like this have one advantage though: People who struggle with the ideas of chance and statistics can develop a sense for the **length of winning and losing streaks**.

**There is a lesson there: **

Just because the past four rounds saw red numbers winning, does not mean that it is now time for a black number. Chance simply does not care.

]]>In short, gambling is wagering on slots, table games and card games. These are available in brick-and-mortar casinos and online. Gambling includes poker games.

Image: Hannamariah (Shutterstock)

Betting is placing money on the outcome of events based on odds given by bookmakers. Horse racing, sports games, political events, TV shows, etc., are examples of bet types offered by bookmakers. Horse racing and soccer are traditionally their highest turnover sports.

However, gambling and betting definitions are much more complicated than the simple definition would suggest. According to the **Ludwig von Mises Institute in Austria**, a bet is “the desire to risk money against another person on the result of an event about the outcome of which we know only so much as can be known.

Thus, people can bet on a wide diversification of events from a general election to a tennis match. Or people might bet on who has the correct answer to a question.

Gambling is the desire to risk money against another person or company on the result of an event that we do not know anything more than is known. Thus, people gamble on services. Many times, gambling and betting are combined. For example, in horse racing, the owner is knowledgeable about the horse and the industry, so he can gamble, but the owner also has to make a bet based on the odds given by bookmakers”, the institute said.

Also, the culture surrounding gambling and betting is expanding and getting more intertwined as more is available online. Soccer betting is popular in Europe and is growing in popularity in the United States. “It works like any other sports gambling options”, said SportsGambling.com.

“Gambling has a long history in the world because outcomes are uncertain”, said Differencebetween.com. “Mankind is interested in knowing the future outcomes whether they are about events in one’s life or games. They put a value on something in the hope of getting more.”

Today, people gamble by betting on sports, playing casino games, betting on horses or visiting an online casino site, such as Harrahscasino.com, ClubWorldCasinos.com and slotter.com.

Historically, gambling is a generic word to describe placing wagers on particular outcomes or events, whilst betting is used to refer to an agreement between two people on whether a prediction will come true.

Governments have tried to regulate gambling to reduce the number of people who are adversely affected by gambling. Today, governments continue to regulate gambling and betting, Differencebetween.com reported.

As more regions and states allow online gambling to take place legally, the lines between the definitions are fusing together. When people visit gambling sites, they deposit a certain amount into a pot. They can either play slots or table games. In some cases, online gambling sites allow the central pot of money to be used to place bets on sports events. Slot machine games online are programmed to look like real games.

For example, Harrahscasino offers customers the chance to play Euro Reels, an online slot game modeled after betting on real soccer games.

According to the site, the game features nine play lines. Three or more scatter icons activate free spins, and scatters can appear anywhere on the game. Customers can win free spins, obtain wild cards that substitute for any symbol and bonus rounds. Players compete against goalkeepers during the bonus Cash Cup with a chance to win the Euro Cash Cup by winning five goals in a row. Every ball kicked into the net is a winner.

Regardless of what term is used, gambling is big business. For example, it represents 1 percent of the gross domestic product of the United States or $14.5 trillion. Economists expect the casino industry to continue growing and supporting the economy. These figures come from betting on sporting events and gambling in casinos or online.

Economists have also compared gambling and betting to investing in the stock market. Investing and gambling both involve risk and choices, reported Investopedia.com. Placing bets is making a choice also. Gamblers and investors have to consider how much to risk on the possible outcome whether it’s a table game or the stock market. Gamblers weigh how much capital is in play or how much money to call a bet versus how much is in the pot. Investors do a similar calculation when determining how possible earning potential of a stock or fund.

]]>Since the growth of online poker caused the average IQ of poker players to increase dramatically it has become even more important to understand the numbers behind the game.

Indeed, while it was once possible for players to make money with a touch of experience and a stoic demeanour, it’s now the statistically minded that rake in vast sums of money at the table.

So, does this mean you need to be like John Nash *(the famous math professor portrayed by Russell Crowe in A Beautiful Mind)* to make money? Fortunately, the answer is “no” because online tools such as the **CardsChat poker odds calculator** are on hand to unravel the poker’s numerical matrix.

Although it can be an advantage to know how to perform complex equations without the aid of a calculator, it’s certainly not a necessity at the poker table.

In fact, given the time you have to make decisions at the felt it’s virtually impossible to accurately work out the exact odds in each scenario. Thankfully, however, the ability to use calculators and other poker tools can help you build up a general appreciation of the numbers involved in various situations.

In the same way you have a kinaesthetic awareness of where your limbs are without having to look at them, using a poker odds calculator often enough allows you to know the right move without having to look at the numbers.

With that said let’s break down the basics of the **CardsChat calculator** and then put it to use in a selection of scenarios.

The main purpose of the calculator is to work out how often a particular hand will win, tie or lose against another, and with this particular piece of software you can compare up to six hands at once.

Once you’ve set the number of hands you want to assess *(you must choose at least two)* you need to highlight the empty boxes and choose the two cards that will make up each hand.

After setting each player’s hand you can hit the “calculate odds” button and the software will tell you how the hands stack-up against each other pre-flop.

Looking at the scenario in the image below you’ll see that when comparing **Ad Kd** against **Jd 9c** the former will be a 65.73% favorite if all the money went in before the flop, and the five community cards were laid out.

Beyond the ability to analyze pre-flop situations you can also assess the winning/losing ratios of hands on the flop and turn. The reason this is useful is because the majority of Hold’em hands don’t start and end before the flop.

Thus, it’s important to **understand how the changing dynamics of the board** affect will alter the win/ lose percentages.