# What are the formats in which odds are presented?

Gambling odds are presented in diverse formats in different places, but they always indicate the same: the potential reward of betting in favor of certain event happening. It is not mandatory to familiarize yourself with all the formats necessarily, only with the ones you need to deal in, however with these, it is highly recommended to grasp an intuitive meaning into what is the implied probability they might be indicating, because sometimes those numbers may be tricking you into believing the implied probability is much higher or much lower than what they actually imply.

## Decimal format and percentage format (implied probability)

*Decimal odds are sometimes called "European odds".*

An odd alone can be interpreted as the promise of giving an even reward for a probability risk. Suppose that the odd for x is 25%, that would mean that if x happens, you will obtain the reward that is even with the assumption that x has 25% chances of happening, this reward can be calculated this way:

1 / 25% = 1 / .25 = 4

That reward is precisely the decimal format, and that percentage is the implied probability. In this case, the decimal odd of 4 means that if you gamble ¤1 and x happens, you will obtain the original ¤1 plus a reward of ¤3, for a total final money of ¤4. This reward is the one that, for an event of such probabilities, would produce in the long term no losses and no earning.

However, the actual probability is usually lower than what is implied, and this lower probability is what allows the bookmaker to make a profit, and makes the naive uninformed player lose money in the long term. However, the bookmaker is not perfect in setting the odds, and sometimes will offer odds better than the even ones, that only the informed strategic player can identify and profit from.

Most bookmakers never present their odds as implied probability percentages, yet it is necessary to understand this format as most of the strategies that exist imply converting the odds into it.

These are the formulas to convert decimal odds to implied probability and vice versa:

d: decimal odd

i: implied probability

d = 1 / i

i = 1 / d

As an example, observe these odds:

x: 1.6 -x: 2.5

They imply a probability of 62.5% for x happening, and 40% for x not happening. As usual, they are not even odds, and the bookmaker is putting a margin in its favor of 2.5 percentage points (as 62.5% + 40% = 102.5%).

## Moneyline format

*Moneyline odds are sometimes called "American odds".*

This format is used mostly in the USA. When the implied probability is below 50%, it indicates the potential per each 100 monetary units bet. When it is , or how much money must be bet to earn 100. In our example, the implied probabilities of x: 62.5% -x: 40% (decimal x: 1.6 -x: 2.5) would become approximately these:

x: -167 -x: 150

These odds mean that, when betting for x happening, you must gamble ¤167 to obtain a return of the same ¤167 plus a prize of ¤100. And when betting for x not happening, if you wager ¤100, and you win, you will obtain the original ¤100 plus ¤150.

The formulas to convert moneyline odds to implied probabilities, and vice versa, when the implied probabilities are lower than 50%, are:

m₊: positive moneyline

i = 100 / (m₊ + 100)

m₊ = 100/i - 100

When the implied probabilities are higher than 50%, the formulas are:

m₋: negative moneyline

i = m₋ / (m₋ - 100)

m₋ = 100i / (i - 1)

Notice that these odds are usually rounded. You must take that into account in cases that requires extra precision.

## Fractional format

*Fractional odds are sometimes called "British odds".*

The fractional format is commonly used in the United Kingdom and Ireland. It represents the net profit (or prize) you will make from a successful bet in relation to your stake. For instance, if the odds are 3/1, this means that for every unit you bet, you will win three units in profit, plus your original bet back.

In our previous example, the implied probabilities of x: 62.5% -x: 40% (decimal x: 1.6 -x: 2.5) would be represented as:

x: 3/5 -x: 3/2

The fractional odds can be easily interpreted by considering the numerator as the potential profit in proportion to the denominator, which represents the initial money gambled. The sum of both gives the total amount you would receive if the bet is successful. The example's odds mean that, when betting for x happening, for every ¤5 you wager, you will win ¤3 plus the original ¤5. And when betting for x not happening, for every ¤2 you wager, you will win ¤3 plus your original ¤2.

It might sound too complex in the beginning, but these numbers can actually serve to visualize the proportions of the earnings. For x: 3/5, per each ¤¤¤¤¤ (¤5) gambled, the prize can be ¤¤¤ (¤3), and the final amout ¤¤¤¤¤¤¤¤ (¤8). Now look at them together:

¤¤¤¤¤

¤¤¤

¤¤¤¤¤¤¤¤

To know the exact prize given any bet, you just need to divide your bet money by the denominator and then multiply it by the numerator. To know the final amount, just add then the original bet to the prize:

¤10 at 3/5 has a prize of ¤10 / 5 * 3 = ¤6 for a final amount of ¤16:

¤¤¤¤¤¤¤¤¤¤

¤¤¤¤¤¤

¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤

¤4 at 3/2 has a prize of ¤4 / 2 * 3 = ¤6 for a final amount of ¤10:

¤¤¤¤

¤¤¤¤¤¤

¤¤¤¤¤¤¤¤¤¤

The formulas to convert fractional odds are these. Understanding fractional odds as composed by a numerator and a denominator:

f: fractional odds

N: numerator of the fractional odds

D: denominator of the fractional odds

f = D/N

Implied probabilities can be obtained this way:

i = D / (N + D)

So, in our example of x: 3/5, -x: 3/2, the implied probabilities would be:

x: 5 / (3 + 5) = .625 = 62.5%

-x: 2 / (3 + 2) = .4 = 40%

However, converting implied probabilities to fractional odds requires a bit more complexity. One method is to assume a value for the denominator and then follow this formula:

N = D/i - D

Then simplify the fraction. It's important to note that the denominator is an assumed value, and the choice of this value may affect the precision of the conversion.

The conversion for x: 62.5% then would be done this way. First suppose a number for the denominator, for example, 100:

D = 100

Then obtain the numerator:

N = 100/.625 - 100 = 160 - 100 = 60

Finally join them and simplify:

F = 60/100 = 6/10 = 3/5

The same method applied to the other option would work this way:

D = 100

N = 100/.4 - 100 = 250 - 100 = 150

F = 150/100 = 15/10 = 3/2

Yet, there is a trick here: the numerator may end up being not an integer. Strictly speaking, there is no mathematical impediment for the fractional odds format to have fractions composed by numbers that are no integers. But the convention is to use only the smallest integers possible, to ease the interpretation of the odds. A simple way to achieve this could be rounding the numerator obtained:

i = 65.4321% =.654321

D = 100

N = 100/.654321 - 100 ≈ 152.830186 - 100 ≈ 52.830186 ≈ 53

F ≈ 52.830186/100 ≈ 53/100

This fractional odd implies a probability of:

i = 100 / (53 + 100) ≈ .65359 ≈ 65.36%

Which is quite close to the number we were aiming at:

.6536 - .654321 = -0.000721

That is just less than a tenth of a percentage point (.0721) below our desired number. Depending on the scenario, this difference might be negligible. However, this imprecision must be taken into account in the particular cases that require high precision.

## Hong Kong format

The Hong Kong odds format is akin to decimal odds, but it only represents the net profit you will make from a successful bet, not including the original money gambled.

In our example, the implied probabilities of x: 62.5% -x: 40% (decimal x: 1.6 -x: 2.5) would be represented as:

x: 0.6 -x: 1.5

These odds mean that, when betting for x happening, for every ¤1 you wager, you will win ¤0.6. And when betting for x not happening, for every ¤1 you wager, you will win ¤1.5.

The formulas to convert Hong Kong odds to implied probabilities, and vice versa, are:

h: Hong Kong odd

i = 1 / (h + 1)

h = 1/i - 1

## Indonesian format

The Indonesian odds format is akin to the American moneyline format, but it uses a base unit of 1 instead of 100.

In our example, the implied probabilities of x: 62.5% -x: 40% (decimal x: 1.6 -x: 2.5) would be represented as:

x: -1.6 -x: 1.5

These odds mean that, when betting for x happening, you must gamble ¤1.6 to obtain a return of the same ¤1.6 plus a prize of ¤1. And when betting for x not happening, if you wager ¤1, and you win, you will obtain the original ¤1 plus ¤1.5.

The formulas to convert Indonesian odds to implied probabilities, and vice versa, when implied probabilities are lower than 50%:

s₊: positive Indonesian odd

i = 1 / (s₊ + 1)

s₊ = 1/i - 1

When the implied probabilities are higher than 50%:

s₋: negative Indonesian odd

i = s₋ / (s₋ - 1)

s₋ = i / (i - 1)

## Malay format

The Malay also uses positive numbers implied probabilities higher than 50% and negative numbers for those under 50%. The positive odds work like the Hong Kong odds, whilst the negative odds work as a number by which the bet must be divided to discover the prize.

The prize and the return of the positive odds, are calculated this way:

y₊: positive malay odd

Prize = bet · y₊

Return = (bet · y₊) + 1

The ones of the negative odds, this other way:

y₋: negative malay odd

Prize = bet / -y₋

Return = (bet / -y₋) + 1

In our example, the implied probabilities of x: 62.5% -x: 40% (decimal x: 1.6 -x: 2.5) would be represented approximately as:

x: .6 -x: -.667

These odds mean that, when betting for x happening, if you gamble ¤1 you will obtain ¤.6 plus your original ¤1:

Prize = ¤1 · .6 = ¤.6

Return = (¤1 · .6) + 1 = ¤1.6

When betting for x not happening, if you wager ¤1, and you win, you will obtain the original ¤1 plus ¤1.5:

Prize = ¤1 / -(-.667) = ¤1 / .667 ≈ ¤1.5

Return = (¤1 / -(-.667)) + 1 = ¤2.5

The formulas to convert Malay odds to implied probabilities, and vice versa, are:

y: Malay odd

For positive odds:

i = 1 / (y₊ + 1)

y₊ = (1 / i) - 1

For negative odds:

i = -y₋ / (1-y₋)

y₋ = i / (i - 1)