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Probability is the likelihood or chance that something will happen. Probability is an estimate of the relative average frequency with which an event occurs in repeated independent trials. Probability gives us a tool to predict how often an event will occur, but does not allow us to predict when exactly an event will occur.

Probability can also be used to determine the conditions for obtaining certain results or the long-term financial prospects of a particular game; it may also help determine if a particular game is worth playing. It is often expressed as odds, a fraction or a decimal fraction also known as a proportion. References can be found on page 24 of the PDF available for download below.

Probability is an estimate of the chance of winning divided by the total number of chances available. Probability is an ordinary fraction e. That means that there are 3 chances of losing and only 1 chance of winning. The true odds are the actual chances of winning, whereas the payout odds are the ratio of payout for each unit bet. A favourite horse might be quoted at odds of 2 to 1, which mathematically would represent a probability of A long shot a horse with a low probability of winning might be quoted at 18 to 1 a mathematical probability of 5.

The true odds of a horse are actually unknown, but most often the true odds against a horse winning are longer a lower chance of a win than the payout odds e. Central to probability is the idea of equally likely outcomes Stewart, Each side of a die or coin is equally likely to come up. Probability, however, does not always seem to be about events that are equally likely. This does not actually contradict the idea of equally likely outcomes. Each of those 27 chances is equally likely.

As another example, in rolling two dice there are 36 possible outcomes: 1, 1 , 1, 2 , 1, 3 , 1, 4 , 1, 5 , 1, 6 , 2, 1. A player rolling 2 dice, however, is most likely to get a total of 7 because there are six ways to make a 7 from the two dice: 1, 6 , 2, 5 , 3, 4 , 4, 3 , 5, 2 and 6, 1. A player is least likely to get a total of either 2 or 12 because there is only one way to make a 2 1, 1 and one way to make a 12 6, 6.

A basic assumption in probability theory is that each event is independent of all other events. That is, previous draws have no influence on the next draw. How could a coin decide to turn up a head after 20 tails? Each event is independent and therefore the player can never predict what will come up next. If a fair coin was flipped 5 times and came up heads 5 times in a row, the next flip could be either heads or tails.

The fact that heads have come up 5 times in a row has no influence on the next flip. It is wise not to treat something that is very very unlikely as if it were impossible see Turner, In fact, if a coin is truly random, it must be possible for heads to come up 1 million times in a row. Even then, the next flip is just as likely to be heads as it is tails. Nonetheless, many people believe that a coin corrects itself; if heads comes up too often, they think tails is due.

To complicate matters, however, there are cases where random events are not completely independent. With cards, the makeup of the deck is altered as cards are drawn from the deck. As a result, the value of subsequent cards is constrained by what has already been drawn. Nonetheless, each of the cards that remains in the deck is still equally probable. If, for example, there are only six cards left in a deck, four 7's and two 8's, a 7 is twice as likely to be drawn as an 8, but the specific card, the 7 of spades, has the same probability of being drawn as the 8 of diamonds.

Another key aspect to computing probability is factoring in the number of opportunities for something to occur. The more opportunities there are, the more likely it is that an event will occur. At the same time, the more tickets purchased, the greater the average expected loss. However, because the expected return is nearly always negative, the player will still lose money, on average, no matter how many tickets the player purchases.

This is true whether the player buys several tickets for the same draw or one ticket for every draw. Adding more opportunities e. One final aspect of probability is the fact that the likelihood of two events occurring in combination is always less than the probability of either event occurring by itself. Friday the 13th, however, only occurs roughly once in days 7 x 30 or once or twice per year. To compute the joint probability of an event, multiply the probability of each of the two events.

It is important to note, however, that the joint probability of two events occurring refers only to events that have not happened yet. Each event is an independent event. Rewards valid for 7 days. Free bets must be placed at min odds of 1.

Exchange free bet limited to certain markets. Payment restrictions apply. You can only take part using one account. If you have been excluded via email or otherwise by Betfair from taking part in sportsbook promotions, you will not qualify for this promotion. Applies to pre-match singles in the Win-Draw-Win market only.

Applies to all online, mobile, phone, and text bets. New customer offer. Exchange bets excluded. Get your single bets paid out if the team you back goes 2 goals ahead - for multiple bets, the selection will be marked as a winner with bet Applies to pre-match single and multiple bets on the standard Full Time Result market for applicable competitions.

Only available to new and eligible customers. The most tangible upside of placing a Double Bet is the potential for a higher pay-out, courtesy of the combined odds. Also, you can hope to back two selections that might be low-value, and still rake in the moolah. You are confident that both these selections will turn up in your favour. When you think about how to work out Double Bet odds, there is an easy equation that you can use. While you can always use this formula and multiply it with your stake to arrive at the returns, you can also choose not to do such heavy lifting.

Simply use an online Double Bet calculator before you place the wager. This is undoubtedly the most straightforward way to calculate your winnings. It is the simplest form of accumulator bet that punters can use to pile up the winnings.

Here, you back the outcomes of two distinctly separate events. You win the bet only if both the selections come through as predicted. You win big, thanks to the combined odds on your selections. You also have the flexibility to back two low-favourite selections. You can place this bet on almost all single sports betting markets.

It is extremely versatile, and all you have to do is back two different selections. Some of the more popular markets ideal for Double Bet include football, horse racing and tennis. The first part goes towards securing a win for your selection, while the other bets on your selection to finish at any of the already-mentioned places. If the selection wins, both parts of the bet return profits. That being said, should you seek to step up your game, a Double Bet may just be the ideal addition to your betting arsenal.

In conclusion, keep an eye out for the latest and the most appetising free bets and promos. You shall thank us later. To know more you can also check out our detailed analysis on system bet. Articles assigned to ThePuntersPage. What Is A Double Bet? By ThePuntersPage. Lots of exciting football betting offers at William Hill! What is Each-way Double Betting? How Does Double Bet Work?

It is wise not to treat something that is very very unlikely as if it were impossible see Turner, In fact, if a coin is truly random, it must be possible for heads to come up 1 million times in a row. Even then, the next flip is just as likely to be heads as it is tails. Nonetheless, many people believe that a coin corrects itself; if heads comes up too often, they think tails is due.

To complicate matters, however, there are cases where random events are not completely independent. With cards, the makeup of the deck is altered as cards are drawn from the deck. As a result, the value of subsequent cards is constrained by what has already been drawn. Nonetheless, each of the cards that remains in the deck is still equally probable.

If, for example, there are only six cards left in a deck, four 7's and two 8's, a 7 is twice as likely to be drawn as an 8, but the specific card, the 7 of spades, has the same probability of being drawn as the 8 of diamonds. Another key aspect to computing probability is factoring in the number of opportunities for something to occur.

The more opportunities there are, the more likely it is that an event will occur. At the same time, the more tickets purchased, the greater the average expected loss. However, because the expected return is nearly always negative, the player will still lose money, on average, no matter how many tickets the player purchases. This is true whether the player buys several tickets for the same draw or one ticket for every draw. Adding more opportunities e. One final aspect of probability is the fact that the likelihood of two events occurring in combination is always less than the probability of either event occurring by itself.

Friday the 13th, however, only occurs roughly once in days 7 x 30 or once or twice per year. To compute the joint probability of an event, multiply the probability of each of the two events. It is important to note, however, that the joint probability of two events occurring refers only to events that have not happened yet.

Each event is an independent event. It is the cumulative and multiplicative aspects of probability that lead people to overestimate their chances of winning. People tend to underestimate the chance of getting one or two of the same symbols on a slot machine because they do not take into account the number of opportunities. A number of studies have shown that people can unconsciously learn probability through experience Reber, Suppose the chances of getting a diamond on a slot machine are 1 in 32 on each of three reels.

Because we occasionally see one 8. The first is an informal folk theory of statistics; the second is a statistical law. These laws can be summarized as follows:. Law of Large Numbers: As the sample size increases the average of the actual outcomes will more closely approximate the mathematical probability.

The law of large numbers is a useful way to understand betting outcomes. In a short trial, heads may easily come up on every flip. The law of averages is an informal approximation of the law of large numbers. The problem with the law of averages, as it is often understood, is that people assume that if something has not happened it is due to happen.

Many people believe that deviations from chance are corrected by subsequent events and refer to the law of averages in support of their belief. The law of large numbers, on the other hand, asserts only that the average converges towards the true mean as more observations are added. The average is not somehow corrected to ensure it reflects the expected average. The key difference is in the expectation. After a streak of 10 heads in a row, the law of averages would predict that more tails should come up so that the average is balanced out.

The law of large numbers only predicts that after a sufficiently large number of trials, the streak of 10 heads in a row will be statistically irrelevant and the average will be close to the mathematical probability. This is still incorrect. According to the law of large numbers, it is not the actual number of flips that converges to the probability percentage, but the average number of flips. Suppose we start by getting 10 heads in a row and keep flipping the coin 1 million times. Does the difference of 10 go away?

In fact, after 1 million flips the number of heads and tails could differ by as much as 1 or 2 thousand. Consequently, the individual cannot use deviations from the expected average to get an edge. It says absolutely nothing about what will happen next or is likely to happen. If the next 40 trials resulted in 19 tails and 21 heads The average converges toward the expected mean, but it does not correct itself.

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