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A guide to odds formats. What are odds, and how does it work

Let us recall that the ratio of probabilities shows whether a given event will happen or not.

In the world of the stakes there are three main odds formats for defining the ration of probabilities:

  1. European (decimal)
  2. American.
  3. British (fractional)

Here we will discuss how the ratio of probabilities is calculated in each system.

1. European Odds (decimals).

The ratio of probabilities presented in decimal system shows the number which should be multiplied by the odds in order to obtain the sum paid by the bookmaker in case of winning. This sum includes the sum of odds plus the gain.

For example:
You make a stake of 20 $ for West Bromwich to beat Manchester United, European (decimal) odds 5.30
If West Bromwich wins, you will receive 20 x 5.30 = 106 $.
Your pure gain is 86 $. / 106-20 /

2. American / US Odds

This system for calculation of the ratio of probabilities differs from both the European and British systems. Here the line is given for both the favourite and the outsider by means of a different ratio.

For the favourite the lines (we can even not call it a ratio of probabilities) is the sum we bet in order to gain 100 units ($). It is set in a negative sign (minus). For example, - 120 means the line of the favourite, which means we should bet 120 $ in order to gain 100 $. The total amount including the sum of bet paid to the bookmaker is 220 $.

For the outsider the line is the sum which we receive as a pure gain if we bet 100 units ($). The line is with a positive sign (plus). For example, +230 means that in case of a bet of 100 $, then we will gain 230 $. In other words the sum paid by the bookmaker is 330 $.

For example:
You make a stake of 20 $ for Arsenal to beat Newcastle
The line for this meeting would be as follows:
For the win of Arsenal - 200
For draw result +275
For the win of Newcastle +500
You make a bet of 20 $ for the win of Arsenal with ratio of probabilities of - 200
Should Arsenal win, you get 20 x (1 + 100/200) = 20 x 1.50 = 30 $.
Your pure gain is 20 x 100/200 = 10 $. / 30-20 /

3. British / UK Odds (fractions)

This system provides the ratio of probabilities as a pure gain but in the format of simple fraction.

For example:
You make a stake of 20 $ for Stoke City to beat Chelsea, UK, British (fractional) odds 5/2.
If Stoke City wins, you will get 20 x (5/2 + 1) = 20 x 3.5 = 70 $
Your pure gain is 20 x 5/2 = 50 $. / 70-20 /

Betting Odds Conversion Table

There are three not so popular systems: Hong Kong, Indonesian and Malaysian systems which are shown in the table below: What one can find out is that the Hong Kong system is similar to the British system, but the difference is that the ratio of probabilities is given in decimal fraction rather than common fraction. The Indonesian system is similar to the American system but divided exactly by 100. The Indonesian system provides that the ratio of probabilities for the favourite complies with the Hong Kong system, and the ratio of probabilities for the outsider shows how many units should be laid down in order to receive a gain equal to one. These are made with negative sign - minus. For example, the ratio of probabilities of -0.67 means that the sum which is laid down is 0.67 $ in order to gain 1 $. In other words the ratio is equal to 1 + 1/0.67 ~ 2.5. Of course these three formants of the ratio are not important to us. These three systems are just tentative.

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