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Probability And Odds

What is probability ?

Probability is a quantitative measure of the likelihood of a given event. If we are certain that an event will occur it is assigned a probability of 100%. If we are certain that an event will not happen it is assigned a probability of 0%. Other events which are neither certain to occur nor certain not to occur are assigned probabilities between 0% and 100%. If an event has a probability of 50% then it is as likely to happen as not to happen. An event with a probability of 10% is not likely to happen while an event with a probability of 90% is likely to happen.

Example 1 Suppose you take a coin from your pocket and toss it in the air. Assuming that it is a fair coin, there are two possible outcomes, heads or tails, and each outcome is equally possible. Therefore, the probability of it being heads is 50% and the probability of it being tales is also 50%.

Example 2 Using a full deck of cards and drawing one card at random the probability of the card being a spade is 1 in 4, there are four suits in a deck of which one is spades. To express this as a percentage you divide the required outcome by the number of possible outcomes and multiply by 100%. So the probability of a spade being drawn at random is (1 / 4) X 100% = 25%

How do odds relate to probability ?

First of all let me explain that there are two ways of expressing odds, fractional odds and decimal (sometimes known as digital) odds.

Fractional odds look like this, 2/1 4/1 11/2

Decimal odds look like this, 3 5 6.5

Odds are simply a way of converting the probability of an event happening into the amount of money you will receive back if you bet on it.

Using the card example above, there is a 25% chance that a spade will be picked at random.

In fractional odds, there are 3 chances you will choose wrongly and 1 chance you will choose correctly, therefore the odds are 3/1. If you put £10 on at 3/1 and are correct you will win 3 X £10 so you will now have £40 as your original £10 is returned for winning bets. To convert a %age to fractional odds divide 100% by the probability %age and subtract 1. In this example,

100% / 25% = 4
4 – 1 = 3

The odds are 3/1

In decimal odds things are much simpler to work out. The odds are simply 100% divided by the probability %age. Using the same card example,

100% / 25% = 4

The odds are 4

Therefore, if you put £10 on at odds of 4 you will now have 4 X £10 = £40.

Below is a table of odds and percentages.

 

Odds And Percentages
%age
Fractional Odds
Decimal Odds
%age
Fractional Odds
Decimal Odds
99.01
1/100
1.01
50
1/1
2
98.04
1/50
1.02
47.62
11/10
2.1
97.06
1/33
1.03
44.44
5/4
2.25
96.15
1/25
1.04
42.11
11/8
2.38
95.24
1/20
1.05
40
6/4
2.5
94.12
1/16
1.06
38.10
13/8
2.63
92.31
1/12
1.08
36.36
7/4
2.75
90.91
1/10
1.1
34.78
15/8
2.88
89.89
1/8
1.12
33.33
2/1
3
87.50
1/7
1.14
30.77
9/4
3.25
85.71
1/6
1.16
28.67
5/2
3.5
84.61
2/11
1.18
26.67
11/4
3.75
83.33
1/5
1.2
25
3/1
4
81.82
2/9
1.22
23.08
10/3
4.33
80
1/4
1.25
22.22
7/2
4.5
77.78
2/7
1.29
20
4/1
5
76.92
3/10
1.3
18.18
9/2
5.5
75
1/3
1.33
16.67
5/1
6
73.33
4/11
1.36
15.39
11/2
6.5
71.43
2/5
1.4
14.29
6/1
7
69.23
4/9
1.44
12.5
7/1
8
66.67
1/2
1.5
11.11
8/1
9
65.22
8/15
1.53
9.09
10/1
11
63.64
4/7
1.57
7.69
12/1
13
61.90
8/13
1.62
5.88
16/1
17
60
4/6
1.67
4.76
20/1
21
57.89
8/11
1.73
3.85
25/1
26
55.56
4/5
1.8
2.94
33/1
34
52.38
10/11
1.91
1.96
50/1
51
50
1/1
2
0.99
100/1
101

Please note that for betting purposes there are no odds for 0% or 100%. This is because if an event has a probability of 100% nobody would take your bet because they are guaranteed to lose. Likewise, if an event has a probability of 0% then you are guaranteed to lose.

There is a quick and simple online tool for converting moneyline, fractional and decimal odds at