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What do you get? Mark the probability on the scale below. You had to work out a probability for roulette, the probability of the ball landing on 7. Here are all the possible outcomes from spinning the roulette wheel. To find the probability of winning, we take the number of ways of winning the bet and divide by the number of possible outcomes like this:. S is known as the possibility space , or sample space. Possible events are all subsets of S. One way of doing so is to draw a box representing the possibility space S , and then draw circles for each relevant event.

This sort of diagram is known as a Venn diagram. Instead of numbers, you have the option of using the actual probabilities of each event in the diagram. It all depends on what kind of information you need to help you solve the problem.

A I is known as the complementary event of A. This gives us. For each event below, write down the probability of a successful outcome. For each event you should have written down the probability of a successful outcome. This event is actually impossible—there is no pocket labeled Therefore, the probability is 0. Q: Why do I need to know about probability? I thought I was learning about statistics. A lot of statistics has its origins in probability theory, so knowing probability will take your statistics skills to the next level.

Probability theory can help you make predictions about your data and see patterns. It can help you make sense of apparent randomness. Q: Are probabilities written as fractions, decimals, or percentages? A: They can be written as any of these. Is there a connection? A: There certainly is. In set theory, the possibility space is equivalent to the set of all possible outcomes, and a possible event forms a subset of this.

Q: Do I always have to draw a Venn diagram? Q: Can anything be in both events A and A I? A: No. The two events are mutually exclusive, so no elements are shared between them. Look at the events on the previous page. Oh dear! Even though our most likely probability was that the ball would land in a black pocket, it actually landed in the green 0 pocket.

You lose some of your chips. The important thing to remember is that a probability indicates a long-term trend only. To work out the probability, all we have to do is count how many pockets are red or black, then divide by the number of pockets. Sound easy enough? Take a look at your roulette board. There are only three colors for the ball to land on: red, black, or green. Calculate the probability of getting a black or a red by counting how many pockets are black or red and dividing by the number of pockets.

If we know P Black and P Red , we can find the probability of getting a black or red by adding these two probabilities together. In this case, adding the probabilities gives exactly the same result as counting all the red or black pockets and dividing by To find the probability of an event A, use.

Q: It looks like there are three ways of dealing with this sort of probability. Which way is best? A: It all depends on your particular situation and what information you are given. Suppose the only information you had about the roulette wheel was the probability of getting a green.

It can still be useful to double-check your results, though. Q: If some events are so unlikely to happen, why do people bet on them? A: A lot depends on the sort of return that is being offered. In general, the less likely the event is to occur, the higher the payoff when it happens. People are tempted to make bets where the return is high, even though the chances of them winning is negligible.

Q: Does adding probabilities together like that always work? A: Think of this as a special case where it does. We might not be able to count on being able to do this probability calculation in quite the same way as the previous one. Try the exercise on the next page, and see what happens. Finally, use your roulette board to count all the holes that are either black or even, then divide by the total number of holes.

When we were working out the probability of the ball landing in a black or red pocket, we were dealing with two separate events, the ball landing in a black pocket and the ball landing in a red pocket. If two events are mutually exclusive, only one of the two can occur. What about the black and even events? The two events intersect.

Calculating the probability of getting a black or even went wrong because we included black and even pockets twice. First of all, we found the probability of getting a black pocket and the probability of getting an even number. When we added the two probabilities together, we counted the probability of getting a black and even pocket twice. To get the correct answer, we need to subtract the probability of getting both black and even.

It includes all of the elements in A and also those in B. Between them, they make up the whole of S. They exhaust all possibilities. On the previous page, we found that. Mutually exclusive events have no elements in common with each other. Draw a Venn diagram for this probability space. How many enthusiasts play baseball in total?

How many play basketball? How many play football? Which sports are exhaustive fill up the possibility space? To find the probability of getting event A or B, use. By adding up the values in each circle in the Venn diagram, we can determine that there are 16 total baseball players, 28 total basketball players, and 16 total football players. The baseball and football events are mutually exclusive. The events for baseball, football, and basketball are exhaustive. Q: Are A and A I mutually exclusive or exhaustive?

A and A I can have no common elements, so they are mutually exclusive. A: Yes it is. It can sometimes be useful to think of different ways of forming the same probability, though. Q: Is there a limit on how many events can intersect? Finding probabilities for multiple intersections can sometimes be tricky. We know that the probability of the ball landing on black or even is 0. The croupier decides to take pity on us and offers a little inside information.

How does the probability of getting even given that we know the ball landed in a black pocket compare to our last bet that the ball would land on black or even. The croupier says the ball has landed in a black pocket. In other words, we want to find out how many pockets are even out of all the black ones.

Out of the 18 black pockets, 10 of them are even, so. It turns out that even with some inside information, our odds are actually lower than before. The probability of even given black is actually less than the probability of black or even. However, a probability of 0. So how can we generalize this sort of problem? First of all, we need some more notation to represent conditional probabilities , which measure the probability of one event occurring relative to another occurring.

So now we need a general way of calculating P A B. Looking at the Venn diagram, we get:. This means that we can rewrite the formula as. The second set of branches shows the probability of outcomes given the outcome of the branch it is linked to. A I refers to every possibility not covered by A, and B I refers to every possibility not covered by B. You can find probabilities involving intersections by multiplying the probabilities of linked branches together.

In other words, you multiply the probability on the first level B branch with the probability on the second level A branch. Probability trees can be time-consuming to draw, but they offer you a way of visualizing conditional probabilities. They drew up a probability tree to show the probabilities, but in a sudden gust of wind, they all fell off.

Your task is to pin the probabilities back on the tree. Here are some clues to help you. Work out the levels. Try and work out the different levels of probability that you need. If you add together the probabilities for all of the branches that fork off from a common point, the sum should equal 1. They drew up a probability tree to show the probabilities, but in a sudden gust of wind they all fell off.

With this probability, you can make no assumptions about whether one of the events has already occurred. You have to find the probability of both events happening without making any assumptions. P A B is the probability of event A given event B. In other words, you make the assumption that event B has occurred, and you work out the probability of getting A under this assumption.

A: No, they refer to different probabilities. When you calculate P A B , you have to assume that event B has already happened. When you work out P A , you can make no such assumption. They look similar. P A B is the probability of getting event A given event B has already happened. P B A is the probability of getting event B given event A occurred. A: Both diagrams give you a way of visualizing probabilities, and both have their uses. It all depends what type of problem you need to solve.

Q: Is there a limit to how many sets of branches you can have on a probability tree? In practice you may find that a very large probability tree can become unwieldy, but you may still find it easier to draw a large probability tree than work through complex probabilities without it. Unfortunately, the ball landed in pocket 17, so you lose a few more chips.

Maybe we can win some chips back with another bet. This time, the croupier says that the ball has landed in an even pocket. We can reuse the probability calculations we already did. Our previous task was to figure out P Even Black , and we can use the probabilities we found solving that problem to calculate P Black Even. So how do we find P Black Even? All we need is some mechanism for finding these probabilities. Use the probabilities you have to calculate the probabilities you need.

Take a look at the probability tree on the previous page. Take another look at the probability tree in So where does this get us? How do you think we can use it to find P Even? The next step is to find the probability of the ball landing in an even pocket, P Even.

We can find this by considering all the ways in which this could happen. These are all the possible ways in which a ball can land in an even pocket. In other words, we add the probability of the pocket being both black and even to the probability of it being both red and even. The relevant branches are highlighted on the probability tree. Can you remember our original problem?

We wanted to find P Black Even where. Putting these together means that we can calculate P Black Even using probabilities from the probability tree. This means that we now have a way of finding new conditional probabilities using probabilities we already know—something that can help with more complicated probability problems. Imagine you have a probability tree showing events A and B like this, and assume you know the probability on each of the branches. Now imagine you want to find P A B , and the information shown on the branches above is all the information that you have.

How can you use the probabilities you have to work out P A B? To find P B , we use the same process that we used to find P Even earlier; we need to add together the probabilities of all the different ways in which the event we want can possibly happen. There are two ways in which even B can occur: either with event A, or without it. This means that we can find P B using:. We can rewrite this in terms of the probabilities we already know from the probability tree.

This means that we can use:. This is sometimes known as the Law of Total Probability , as it gives a way of finding the total probability of a particular event based on conditional probabilities. We started off by wanting to find P A B based on probabilities we already know from a probability tree. What we need is a general expression for finding conditional probabilities that are the reverse of what we already know, in other words P A B.

And even though the formula is tricky, visualizing the problem can help. The Manic Mango games company is testing two brand-new games. Manic Mango selects one of the volunteers at random to ask if she enjoyed playing the game, and she says she did. If you have two events A and B, then. If you have n mutually exclusive and exhaustive events, A 1 through to A n , and B is another event, then. It will give you the same result, and it can keep you from losing track of which probability belongs to which event.

Did we make a mistake? This means that P Even Green is 0; therefore, it has no effect on the calculation. Is that always the case? They are two separate probabilities, and making this sort of assumption could actually cost you valuable points in a statistics exam. For example, it can be used in computing as a way of filtering emails and detecting which ones are likely to be junk. Before you leave the roulette table, the croupier has offered you a great deal for your final bet, triple or nothing.

If you bet that the ball lands in a black pocket twice in a row, you could win back all of your chips. Notice that the probabilities for landing on two black pockets in a row are a bit different than they were in our probability tree in Bad luck! Take a look at the equation for this probability:. For P Even Black , the probability of getting an even pocket is affected by the event of getting a black. We already know that the ball has landed in a black pocket, so we use this knowledge to work out the probability.

We look at how many of the pockets are even out of all the black pockets. To work out P Even , we look at how many pockets are even out of all the pockets. P Even Black gives a different result from P Even. In other words, the knowledge we have that the pocket is black changes the probability.

These two events are said to be dependent. Look at the probability tree on the previous page again. What do you notice about the sets of branches? Are the events for getting a black in the first game and getting a black in the second game dependent? Not all events are dependent. Sometimes events remain completely unaffected by each other, and the probability of an event occurring remains the same irrespective of whether the other event happens or not.

What do you notice? These two probabilities have the same value. In other words, the event of getting a black pocket in this game has no bearing on the probability of getting a black pocket in the next game. These events are independent.

If one event occurs, the probability of the other occurring remains exactly the same. If events A and B are independent, then the probability of event A is unaffected by event B. In other words. We can also use this as a test for independence. If A and B are mutually exclusive, then if event A occurs, event B cannot. Free Stock Photo. You can bet on it like any other individual number, but if the number 5 is spun then only the bets on 5 win and all other bets lose.

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Another result of this, is that the ball will hit some metal deflectors more often than others. The French Roulette table is the most different ones as it has a slightly different layout and it features the bet names in French. In French casinos 'American Roulette' means a roulette game with double zeros 0, 00 - on the table layout and on the wheel , the same as used in the USA. Traditional European Roulette Table perspective vector illustration roulette close up Traditional European Roulette Table perspective vector image roulette table poker duisburg open illustration Vector realistic casino roulette table, wheel and chips top view isolated on green background Casino Digital Roulette Casino roulette table perspective illustration.

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Still, these are only superficial differences that do not impact the return-to-player ratio. Final 2 means buy bitcoin casino software bet on the numbers 2, 12, 22 and 32 straight up four chips. Single-zero European wheel: Related Searchesroulette tableamerican rouletteGreat gambling information site Use casino eslava plaza castillo the ' Main Menu' on image roulette table the right margin to explore this site.

Casino Gambling Roulette Wheel. As a professional roulette player, the first and most critical thing to understand is that there is a big difference between the roulette table and the wheel. The roulette wheel layout and the roulette table layout are a deliberate randomisation. Although you could argue on the American 00 wheel, at around 00 there is a slightly higher average of red pockets, and at around single zero, there is a slightly higher average of black pockets.

But the difference is not significant. Steve Bourie, author of the American Casino Guide, explains how to play and how to win at roulette. Topics covered include: the various bets that can be made; the casino's advantage on those bets; the worst bet you can make; the difference between double-zero and single-zero roulette tables; finding the best roulette games to play; and much more.

The wheel is the battlefield. It is the court that judges the outcome without possibility for an appeal. The fixed point of the horizon on which every roulette player has his eyes full of anticipation. A slight difference, a minor game of the wheel, one number left or right, can decide ruin from victory. The wheel is the game. The roulette cylinder was introduced in a primitive form, in the 17th century, by Blaise Pascal, a French physicist, philosopher and inventor, in his quest to create for a perpetual motion machine.

The game of roulette as we know it today started being played a century later, around , in France. For the untrained eye, there is no difference between the different types of roulette wheels, but at a closer look, the differences become self-evident. One of the first decisions that roulette players need to make is whether to spin a European or American roulette, as these are the two main types of roulette wheels.

One big difference between them is that the American version has two zeroes on the cylinder, which leads to a bigger advantage for the casino. This should have a deterring effect on prospective players, but there are still plenty who choose this type of wheel, mainly because in some countries like the USA there are no alternatives, as the vast majority of casinos houses only double zero wheels. Interestingly the first roulette introduced in France had two zeros, but that changed when the German casinos wanted to compete and introduced the single zero roulette to attract more clients.

Please note that except the different types of wheels there are also different types of tables and rules variations. They are the only bets that are not based on the layout of the table, but on the layout of the wheel. Here is a list of all such bets, along with the numbers they cover.

Find high-quality stock photos that you won't find anywhere else. Types of pockets. Many free stock images added daily! Refer to the second image and the below for an explanation of the types of bets:. The American version of roulette is known for having the highest casino. With its addition, the total number of pockets on the American roulette wheel become

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You can bet on any of these squares, or a combination of them, linked by the grid lines that form between them — rows, two neighboring squares, four squares, for example. Further, 18 of the numbers are red, with the remainder are black. You can also bet on the number being or , plus on the winning number being in a particular section of the table. And how is this winning number determined? By spinning the white ball within the rotating roulette wheel. European Roulette is perhaps the most popular version of roulette in land-based and online casinos.

You have the 36 regular numbers, split into columns of 12, and sitting on top is a single, green zero. This is what gives the casino its house edge. But the key thing is if zero comes in, then everyone who bet on any other number, red or black, or odd or even, loses their money.

The Europeans always claim Americans like to do things bigger and better. Well, in the case of roulette, America added a second green zero segment, with a double zero this time. From a player point of view, the odds in American roulette are worse.

Now you still get 36 numbers to choose from, but you also have the two zero segments to get in the way. One other noticeable difference to European Roulette, although it does not alter the odds, is that the order of the numbers on the wheel is different in American roulette.

The French actually do the players a favor. Like European roulette, there is only one green zero segment. Alternatively, there may be the En Prison rule. Here, all the chips are locked in place on red or black, or odd or even for another spin.

If you win that, then you get your chips back. These bets split the table in half, with one bet allowing you to bet on all of the lower half of the numbers and the other half allowing you to bet on all of the higher numbers Also known as the "low bet" and "high bet". The dozen bet allows players to bet on 3 different sections containing 12 numbers, which are; , and This bet offers slightly higher odds than an even money bet, but the chances of winning on one spin are a little lower.

The column bet is very similar to the dozen bet, but instead splits the table into 3 sections length-ways rather than side-ways. Each of these bets also offer odds of , just as with the dozen bets. This particular bet is not always available at online casinos, but can still be played at the majority of them. Often overlooked by many novice players, this bet allows you to bet on 6 numbers at a time via a bet split between two adjacent rows. Note: This bet can only be placed on American roulette tables ones with the green The "five number bet" holds the title for the worst bet in roulette.

The house edge for this bet is 7. Every other bet on a double-zero roulette has a house edge of 5. If you're playing American roulette — which you shouldn't be anyway — avoid this bet. Also known as a "square bet" or "corner bet". The 4 number bet allows you to bet on 4 adjoined numbers at a time. The chances of hitting any of these numbers is relatively low, but there is a decent payout for when you get lucky.

This bet involves similar placement to that of the 6 number bet, except for the chip is placed on the edge of one row, rather than spread across two. This bet is also known as the "street bet" or "stream bet". You can also place 3-number bets at the top of the table using the green zero s. These can be placed in both single-zero and double-zero roulette, although you have an extra 3-number bet in double-zero roulette courtesy of that extra 00 number.

The payouts and probability for this bet are the same for the respective roulette tables as the street bet above. This is where the odds start to get pretty big. A 2 number bet or "split bet" allows you to bet on two adjacent numbers, offering you some pretty attractive odds of - the second biggest payout available at a roulette table.

You can place a split bet across two numbers vertically or horizontally if that makes any sense. The single number bet or "straight bet" is the big one, offering the greatest payouts at the roulette table of Simply place your bet on one number and hope to get lucky.

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D - 4 numbers with 0 and 4 Corner. E - 6 numbers, 6 Line. Outside bets: F - 12 numbers, Column. G - 12 numbers, Dozen. Finales - A type of group bets on numbers ending with the same digit. Examples: Final 7 means bet on the numbers 7, 17 and 27 straight up three chips. Final 2 means bet on the numbers 2, 12, 22 and 32 straight up four chips. The table layout on the French version of roulette is different from the American style roulette table shown above. The main difference is in the position of the side bets outside bets.

The side bets on the French table are split in two and run along both sides of the table layout. Each side bet is given its French name and sometimes also its English translation underneath. Roulette Announced Bets or Call Bets Used in French roulette tables and in some European casinos with single-zero wheel roulette tables. Common in most UK casinos with single-zero wheel American style roulette tables.

Roulite or Roulight table layout Roulite or Roulight is the modern variety of Roulette. A table game that has been developed in the first instance by specialists at the Wiesbaden Casino, Wiesbaden, Germany. The game is dynamic and very fast. Players, who like to play sectors and neighbours love it. Bets can only be placed on full numbers staight up , on two connected numbers split , neighbours of numbers and sections of the wheel.

No outside bets. La Boule table layout and wheel Boule or La Boule is a simple and fast game that is similar to Roulette, popular in French casinos and can now be played online. The game features a table and a wheel with only 9 numbers and 3 different colours. The wheel is spun and a small rubber ball bounces around the wheel before settling into one of the coloured holes to determine the outcome.

Betting will be familiar to Roulette players with the table layout providing a range of betting options. The number 5, coloured yellow, plays in a similar way to the zero 0 or 00 in normal Roulette. You can bet on it like any other individual number, but if the number 5 is spun then only the bets on 5 win and all other bets lose. Because there are less numbers in Boule, the chances of spinning a 5 are greater than a zero being spun in normal Roulette, which makes the house edge of La Boule higher than Roulette.

If you bet on the winning number then you are paid , which is the payout for all bets on individual numbers, and on all other bets. Seven additional betting circles are added to the regular table layout, located among the outside bets as shown on the photo below. How it works: A set of electronic numbers, independent from the roulette wheel numbers, act as a secondary wheel on the electronic billboard display along with a set representing the actual roulette wheel numbers, forming two concentric rings spinning in opposing directions, as shown on the billboard display photo below.

When "no more bets" is announced, the two rings on the display stop, randomly aligning the two sets of numbers. This takes place before the ball on the actual roulette wheel comes to a stop and lands on the winning number. When the ball stops, the corresponding winning number on the display ring is then paired with its aligning electronic number. The sum of these paired numbers determines the spread-bet result.

The Neighbors Bet is popular with people who chase hot and cold sectors of the wheel. The house advantage is the same as for all other European Roulette bets 2. Your payout will be on the number that comes in and it will depend how many neighbours you bet to know your return. This is also quite a neat way of mixing it up a bit if you are playing even money bets bet 8 Neighbours.

Test them out when you sign up at one of our recommended casinos- just make sure you turn on the advanced betting mode. Play Neighbours Bet Neighbors at these Casinos 1. Good for Microgaming Roulette specialist 32 Red is a roulette number! Play Roulette Visit 32red.