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Odds are also used to describe the chance of an event occurring but they compare the number of ways it can occur to the number of ways it cannot occur. Sometimes, when it comes to expressing the odds of a particular bet in roulette, they would be in reverse, indicating the odds against winning. Using the same example, the odds of the number 17 against winning would be , or 36 to 1.

There is a huge difference between the two terms, but it will be explained in detail in the following section. If we place our chips on red, the probability would be 18 out of 37, while the odds would be against us because there would be 19 ways to lose against 18 ways to win. When determining whether a roulette bet has good or bad odds, experienced players take into account not only their probability of winning and the true odds but also the potential reward they could bring.

Each bet pays out differently, depending on its likelihood of winning — the less likely a given outcome is to occur, the more its potential payout would be. There is a sound logic behind this and in a perfect world where casinos would not have to make a profit, the payout of every bet would be equal to the odds against winning.

Let us take a look at the straight bet in European roulette — the odds against the player here are 36 to 1 because as we have already shown above, there are 36 ways for this bet to lose and only 1 way to win. In order to offer a reward that would match the risk, the casino would be expected to pay players 36 to 1. In other words, it would be expected to return the original stake and to pay out winnings that are worth 36 times the amount of the bet.

Casino Odds Additional Tips In reality, this does not happen, however, and the house gives a slightly lower payout of on winning straight-up bets. The idea is that on every winning wager, players pay a small fee to the casino and in this case, it is one unit.

The difference does not seem significant but it is how casinos gain their advantage over players — by paying every winner just slightly less than they should have. Over time, this tiny difference makes a large profit for the house and provides a guaranteed income in any possible scenario. And while both are expressed as ratios of two numbers, they are never equal — the odds against winning are always slightly higher than the casino odds. The closer the casino odds get to the true odds of any given bet, the lower the advantage of the casino.

Clearly, the payout does not correspond to the true odds of roulette bets. The same concept applies to all bets in the game, which results in an average house edge of 2. There are several formulas for calculating the house edge but probably the simplest one is the following — we need to subtract the casino odds from the true odds against success and then, to multiply that by the probability of success.

So, the formula will look like this:. To express it as a percentage, we multiply by and get 2. Several other formulas exist, but they all eventually come to the same conclusion and percentage for the house edge. Roulette House Edge Additional Tips What this means for the players is that they can expect to lose 2. Of course, this is a theoretical ratio between the stake and the expected loss but things could be very different in real life.

So, the house edge can only get closer to reality with hundreds or even hundreds of thousands spins of the roulette wheel. It is a theoretical concept and while this may sound too vague to players, it is a good indicator of how much money they can expect to lose over time. Of course, they might win hundreds of dollars by the end of one gaming session or lose hundreds more in the next one. Still, they are less likely to lose their bankroll if they stick to specific games and bets where the casino has the lowest advantage.

The idea that by using a complex strategy one could beat the odds in roulette is very popular but equally misleading. There are countless guides, books, and websites dedicated to convincing people that there is a guaranteed method of winning in this game. Unfortunately, these methodologies have been repeatedly proven to be inefficient in securing winnings over the long term. Moreover, their short-term usefulness is doubtful and the reason is obvious to most expert-level players — roulette is a game with fixed odds that cannot be changed even with the best strategy.

As explained above, the outcome of every spin of the roulette is random and based on probability. The house edge, therefore, also remains the same almost as a proof for the popular saying that the house always wins. The so-called roulette strategies are, in their essence, betting systems based on a progression where the amount of the stake changes after a certain outcome. There are also systems where the bet is decreased, while in others, it remains the same throughout the entire game session.

Overall, the idea is to help players minimize their losses or even generate some decent winnings over the long term. While none of these betting progressions provides a fool-proof way to win, another type of strategies comes with exactly this claim.

These strategies are based on the notion that you can increase your chances of winning by covering a large part of the table. This strategy, however, will be too costly for most players, especially after a few losing spins. Placing neighbor bets or any other type of announced bets could be detrimental to those who are not well prepared to suffer serious losses.

In conclusion, even the best methods and combinations of bets cannot aid you in beating the odds and overcoming the built-in casino advantage. Some roulette players rely on quite different methods for securing winnings. Known as advantage play methods, these include any strategies that give players either a statistical or a mathematical advantage over the casino. If employed successfully, they can beat the standard roulette odds and even if it is just by a little, it should be enough to provide players with long-term winnings.

Unlike the betting strategies and systems described above, advantage play does not revolve around the betting layout but rather, around the wheel. It can be used in both online and land-based casinos and online, advantage players would try to use special software that records and analyzes the results of hundreds of spins.

The aim is to find a pattern in the winning numbers such as repeating sequences of winning numbers and then, to use it to make predictions. However, most online casinos nowadays offer roulette games based on RNG random number generator so finding patterns would be impossible as the outcome of every spin is random. When it comes to playing a roulette game with a physical roulette wheel , however, advantage play is much more different.

Players who try to use this technique would typically stand by the roulette table for at least spins and write down all the winning numbers in the hope that they would be able to spot numbers that come out more frequently than others. 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. In other words, if two events are independent, then you can work out the probability of getting both events A and B by multiplying their individual probabilities together.

As the events are independent, the result is. If A and B are mutually exclusive, then if event A happens, B cannot. Also, if event B happens, then A cannot. If A and B are independent, then the outcome of A has no effect on the outcome of B, and the outcome of B has no effect on the outcome of A. Their respective outcomes have no effect on each other. Q: Do both events have to be independent?

Can one event be independent and the other dependent? Q: Are all games on a roulette wheel independent? A: Yes, they are. Separate spins of the roulette wheel do not influence each other. In each game, the probabilities of the ball landing on a red, black, or green remain the same. How do I use a Venn diagram to tell if events are independent?

Venn diagrams are great if you need to examine intersections and show mutually exclusive events. The Case of the Two Classes. The Head First Health Club prides itself on its ability to find a class for everyone. As a result, it is extremely popular with both young and old. The Health Club is wondering how best to market its new yoga class, and the Head of Marketing wonders if someone who goes swimming is more likely to go to a yoga class.

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Game weighting applies. We have noticed that many of our players like a flutter on the horses or the football. With that in mind, welcome to our sports betting section to help you find the best places to have a bet! Many of the casinos that we feature here on the site have decent sportsbooks, such as Betway, Ladbrokes, Paddy Power and bet I guess many people who like a flutter on roulette also like to bet on sports.

Generally they offer mini European roulette games. When you are looking for a bookmaker, the bonus is an important consideration, of course, but you should also use other criteria. The obvious place to start, is to make sure that the bookie offers bets on the sport that you are interested in, particularly if you are looking at less mainstream markets like betting on the Hong Kong Rugby Sevens.

If you want to bet on the football or the horse- well they all cover those sports, but check that they include your favourite team, competition or race. Choosing a good online bookie is more complicated than choosing an online casino- there are just more variables to consider. If you are already signed up with an online casino, and they have a sportsbook, then it makes sense to try their sports service out if they operate a single wallet where you can transfer and access your funds acorss all of their services.

In most sportsbooks, you can choose whether to display the odds as a fraction or as a decimal. In both cases, the odds tell you the payout of the bet. You are more likely to see decimal odds at betting exchanges like Betfair, but most bookies will let you customise the site so that the odds are shown in the format that you prefer. If a bet has odds of 9. This is pretty easy- you have just got to remember that decimal odds include your bet, so are always higher.

Add one and you get to 3. Which is better? Well, in decimal, they are 3. The other way that you might see odds displayed is as American Odds. Decimal odds show the total amount you will get back if your bet wins for every 1 unit you stake. Unlike other types of odds, decimal odds always include the initial stake in the return rather than just the profit. With decimal odds, 2. This means that you would double your money if you were to place a bet at 2.

Anything under decimal odds of 2. Anything above decimal odds of 2. The majority of online bookmakers have built in functionality on their websites to allow you to easily change the format of odds should you wish to. This is usually found either in your account settings or as an option to choose from when looking at the available bets via a drop-down box.

This takes the hard work out of manually converting odds as the websites do it for you automatically. Should you wish to convert decimal odds to fractional though, this can be done by:. As well as their widespread use, decimal odds make it easy to calculate your return by simply multiplying the decimal odds on offer by the amount you are betting. This makes it particularly useful if you like to place doubles, trebles or other larger accumulators as all you need to do is multiply the odds of each leg in your accumulator then multiply this by the stake.

Decimal odds also make it very easy to find the best price when comparing the same bet across multiple bookmakers, unlike other odds formats. The best odds are represented by the highest number — find the biggest number and you know that you will get the best return for your stake.

This means that you would double your money if you were to place a bet at 2. Anything under decimal odds of 2. Anything above decimal odds of 2. The majority of online bookmakers have built in functionality on their websites to allow you to easily change the format of odds should you wish to.

This is usually found either in your account settings or as an option to choose from when looking at the available bets via a drop-down box. This takes the hard work out of manually converting odds as the websites do it for you automatically.

Should you wish to convert decimal odds to fractional though, this can be done by:. As well as their widespread use, decimal odds make it easy to calculate your return by simply multiplying the decimal odds on offer by the amount you are betting. This makes it particularly useful if you like to place doubles, trebles or other larger accumulators as all you need to do is multiply the odds of each leg in your accumulator then multiply this by the stake. Decimal odds also make it very easy to find the best price when comparing the same bet across multiple bookmakers, unlike other odds formats.

The best odds are represented by the highest number — find the biggest number and you know that you will get the best return for your stake. As decimal odds usually are written to two decimal places, this provides the bettor with even more accuracy. Decimal Odds Decimal odds are the standard and most popular method for specifying odds across the globe, particularly in Europe, Canada and Australia. Should you wish to convert decimal odds to fractional though, this can be done by: 1 Writing down the decimal divided by 1, e.

Choosing a good online bookie is more complicated than choosing an online casino- there are just more variables to consider. If you are already signed up with an online casino, and they have a sportsbook, then it makes sense to try their sports service out if they operate a single wallet where you can transfer and access your funds acorss all of their services.

In most sportsbooks, you can choose whether to display the odds as a fraction or as a decimal. In both cases, the odds tell you the payout of the bet. You are more likely to see decimal odds at betting exchanges like Betfair, but most bookies will let you customise the site so that the odds are shown in the format that you prefer. If a bet has odds of 9. This is pretty easy- you have just got to remember that decimal odds include your bet, so are always higher.

Add one and you get to 3. Which is better? Well, in decimal, they are 3. The other way that you might see odds displayed is as American Odds. You can select this on bet, for example. The odds next to the handicap shows the payout. Under this handicap, a win to Leicester is seen as the expected result equivalent to a draw. If the score is to Leicester as expected, you get a refund. If that all seems too complicated, give it a wide berth and just stick to simple win or lose bets!

This is the Other Big Innovation in sports betting, particularly with the rise of mobile betting. You can bet In-Play at most bookmakers now, on the bigger events. Which means that they offer dynamic odds as the match or race is taking place.

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