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Bettors should always look for a mathematical edge rather than rely on their impulses. Learning how to use the Kelly Criterion, for example, is a great way for bettors to determine how much they should stake. Read on to find out.

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Prior to placing a bet bettors should consider six important questions: who, what, when, where, why and how? But for this article, it is the how, as in how much to bet, we are interested in.

Popular staking method which suggests that stake should be proportional to the perceived edge.

Consider placing a bet on the English Premier League. We can adapt these questions accordingly:

• Who to bet on? Manchester United
• What to bet on? Top 4 finish
• When to bet on? Now
• Where to bet on? Pinnacle tend to offer the best odds
• Why to bet on? They seem to be under-priced
• How much? How much to bet on this outcome?

Most articles focus on the first five questions, typically using mathematical or statistical justifications on answering ‘why’ - such as the article on how to use Monte Carlo methods.

In making financial decisions, the key issue is not only finding the adequate financial products to invest in but also deciding how to subdivide one’s portfolio. Similarly, an important question for a bettor, is how much to wager?

Many papers recommend using the Kelly Criterion or a derivative of it - such as my 2013 paper appearing in the The Journal of Gambling Business and Economics. In essence, the Kelly Criterion calculates the proportion of your own funds to bet on an outcome whose odds are higher than expected, so that your own funds grow exponentially.

B = the Decimal odds -1
P = the probability of success
Q = the probability of failure (i.e. 1-p)

Using a coin as an example of Kelly Criterion staking

For example, consider you are betting on a coin to land on heads at 2.00. However, the coin is biased and has a 52% chance of ending up on heads.

In this case:

P= 0.52
Q = 1-0.52 = 0.48
B = 2-1 = 1.

This works out at: (0.52x1 – 0.48) / 1 = 0.04

Therefore the Kelly Criterion would recommend you bet 4%. A positive percentage implies an edge in favour of your bankroll, so your funds grow exponentially. You can also test the criterion for different values in this online sheet by using the code below.

Ultimately the Kelly Criterion offers a distinct advantage over other staking methods such as Fibonacci and Arbitrage methods as there is a lower risk. However, it does require precise calculation of the likelihood of an event outcome, and discipline of this method will not provide explosive growth of your bankroll.

Keep up-to-date with more top-notch betting articles by following us on Twitter @PinnacleSports.

The odds converter tool in this page will convert odds from any of the three main formats into the other formats.
It will also calculate the relevant implied probability too.
To use it, simply enter the odds you wish to convert in the appropriate box, and then click the “Convert Odds” button. It’s as easy as that!

If you came to this page specifically looking for a tool to
convert odds, then it’s likely that you already have a
fundamental understanding of what odds are and how they work in
relation to sports betting. If this is a subject that you’re not
particularly familiar with, however, then you might want to read
the following article from our beginner’s guide to sports
betting.

Overview of Different Odds Formats

If you live in the United States, then simply knowing the
moneyline odds will suffice, as this is the primary format used
by the limited number of gambling sites available for US
residents. Likewise, if you live in the United Kingdom, then you
only really need to know how fractional odds work. If you live
in Europe, then the decimal format is the one that will be most
important for you to understand.

With all that being said, it’s still a good idea to be
familiarized with how each format works. Many online betting
sites will allow you to choose the format that their odds are
displayed in. Please keep in mind that the conversation may
round in their favor.. For example, most US friendly sites offer
moneyline odds of -110 when betting points spreads. If you
choose to bet in the decimal format instead, then you’ll often
be given odds of 1.90. The true conversion is 1.9091 though, so
you’ll potentially lose a small percentage of your winnings if
you bet based on their conversion.

Therefore, it can be an advantage to use the primary format
offered by an online bookmaker, which is why it pays to make
sure you understand each of the different formats. We’ve
explained them all below for you.

American Odds/Moneyline Odds

Odds in this format are expressed as either a positive number
or a negative number. When they are a positive number, the
number represents how much in winnings is paid per $100 staked.
The following examples illustrate how positive moneyline odds
work.

When they are a negative number, the number represents the
amount of money that needs to be staked in order to win $100.
The following examples illustrate how negative moneyline odds
work.

Please see our article on calculating payouts from moneyline
odds for details on how to work out the potential winnings from
wagers using this format.

Decimal Odds

This is the most popular odds format outside of the United
States and is sometimes referred to as European odds. It’s a
very simple format where the odds are expressed as a single
positive number, usually to two decimal places. This number
states how much a winning bet returns (including the initial
stake) for each unit wagered. The following examples illustrate
the decimal format in practice.

Our article explaining how to calculate payouts from decimal
odds will teach you how to work out the potential returns from
wagers placed using this format.

Fractional Odds

Fractional odds are mostly used in the UK, but lately the
decimal format has been becoming more popular. Odds in this
format are displayed as a fraction, as the name suggests. The
first number of the fraction shows how much you can win per the
second number staked. This sounds more complicated that it
actually is and the easiest way to understand this format is
simply to look at some examples.

Please note that when the second number of the fraction is
higher than the first, it means the odds are less than even
money. This is referred to as odds on (as opposed to odds
against), and is the equivalent of when moneyline odds are a
negative number or when decimal odds are a number less than 2.

Odds Conversion Math

Our conversion tool is the easiest way to change odds between
formats but there will be times when you don’t have access to
it. When you’re at a Las Vegas sportsbook or a high street
bookmaker, you may need to be able to do these conversions in
your head. For this reason, we’ll run through the math required
to convert each format into all of the other formats.

Converting Moneyline Odds

To Decimal

The calculations required to convert from moneyline odds
changes depending on whether the odds are positive or negative.
To convert positive odds into decimal odds, the following
calculation is required.

Sports Betting Simplified Calculator

Example: Converting +175

(+175 + 100) / 100 = 2.75

For negative odds, we ignore the minus symbol and use the
following formula.

Example: Converting -110

(110 + 100) / 110 = 1.909

To Fractional

When converting from the moneyline format into the fractional
format, the calculations again depend on whether the odds are
positive or negative. To convert positive odds, you simply
create a fraction by putting the relevant number over 100 and
then simplifying the fraction if possible.

300/100 is simplified to 3/1

To convert negative odds, you create a fraction by putting
100 over the relevant number (ignoring the negative sign).
Again, you then need to simplify the fraction if possible.

100/110 is simplified to 10/11

Converting Decimal Odds

To Moneyline

The method required to convert the decimal format over to the
moneyline format is dependent on whether the odds are greater
than 2.0 or not. We’ll look at how to convert odds of 2.0 or
less first. To start with, you have to carry out the following
calculation.

After doing this calculation, the odds are rounded and a
negative sign must be added.

100 / (1.95 – 1) = 105.25

To convert odds of greater than 2.00, you must start with the
following calculation.

To convert odds of greater than 2.00, you must start with the following calculation.

You then add a positive sign to the result, as shown in this
example.

(2.45 – 1) x 100 = 145

Positive sign added = +145

To Fractional

The first step in converting from decimal to fractional
format is to create a fraction by using the formula.

This will often create a fraction that includes a decimal,
which isn’t a proper fraction. To overcome this, the next step
is to multiply both sides of the fraction by 100. Finally, the
fraction needs to be simplified. The following example
illustrates this better than any written explanation can.

Sports Betting Simplified Games

(1.45 – 1) / 1 = 0.45/1

Multiply both sides by 100 = 45/100

Simplified = 9/20

Converting Fractional Odds

Before we get into the math involved here, you need to
understand the terms numerator and denominator. In this context,
the numerator is the first number in the fraction and the
denominator is the second number in the fraction. With odds of
2/1, for example, 2 is the numerator and 1 is the denominator.

To Moneyline

There are two methods needed for converting from the
fractional to the moneyline format. The first is for when the
numerator is greater than the denominator. The following formula
needs to be used in the beginning.

A positive sign then needs to be added to create the
moneyline odds, as per the following example.

Sports Betting Simplified Game

(6 / 4) x 100 = 150

Positive sign added = +150

The second method is for when the denominator is larger than
the numerator. In these cases, the following formula needs to be
used.

A positive sign then needs to be added to create the correct
moneyline odds. This is illustrated in the following example.

100 / (2 / 5) = 250

Negative sign added = -250

To Decimal

Converting odds from the fractional format to the decimal
format is relatively simple and it requires just the following
formula.

(11 / 10) + 1 = 1.10

Implied Probability Explained

Sports Betting Simplified Rules

Implied probability in relation to sports betting is
basically the implication of the odds as it relates to the
chances of an outcome happening. We’ll cover this in more detail
shortly, but first let’s look at how to calculate it. It’s
easiest to determine implied probability from odds in the
decimal format, using the following simple formula.

Sports Betting Simplified Poker

What this example shows us is that the implied probability of
2.50 odds is 0.40 (or 40% if expressed as a percentage). This
means that odds of 2.50 on any possible outcome imply that the
chance of that outcome happening is roughly 40%. So if, for
example, a tennis player is at 2.50 to win an upcoming match,
the implication is that he has a 40% chance of actually winning
that match.

You can read more about implied probability in this article on probability in sports betting. The article also
covers expected value, which is a related topic that you should definitely learn about if you want to be a
successful bettor.

Understanding Vig

When looking at the odds set by bookmakers, it’s important to
recognize that implied probability is rarely an entirely
accurate reflection of the real chances of a wager winning. This
is because bookmakers always try to set the odds at levels that
are lower than they actually should be in relation to real
probability. If their view was that a soccer team had a 60%
chance of winning a match, for example, they wouldn’t offer odds
that exactly reflected that chance. Their odds would be lower,
as this is how they make money successfully.

By reducing the odds relative to the probability of an
outcome happening, bookmakers effectively charge a commission
for every wager they take. This commission is known as vig,
which is short for vigorish. It can also be referred to as the
overround or juice. It’s similar in some respects to the house
edge in casino games and it’s basically what gives the
bookmakers an advantage over their customers.

What sets the bookmakers’ advantage apart from the casinos’
advantage is that, unlike the house edge, it can be overcome. In
order to overcome it, though, you first need to understand
exactly how vig works and the effect it has in sports betting.
You should visit our page on the subject of how bookmakers make
money, as this is all about the methods that bookmakers use to
ensure they are profitable. Charging vig is one of these methods
that we explain thoroughly.