Probabilty 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.
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.
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.
| %age | Fractional Odds | Decimal Odds |
|---|---|---|
| 99.01 | 1/100 | 1.01 |
| 98.04 | 1/50 | 1.02 |
| 97.06 | 1/33 | 1.03 |
| 96.15 | 1/25 | 1.04 |
| 95.24 | 1/20 | 1.05 |
| 94.12 | 1/16 | 1.06 |
| 92.31 | 1/12 | 1.08 |
| 90.91 | 1/10 | 1.1 |
| 89.89 | 1/8 | 1.12 |
| 87.50 | 1/7 | 1.14 |
| 85.71 | 1/6 | 1.16 |
| 84.61 | 2/11 | 1.18 |
| 83.33 | 1/5 | 1.2 |
| 81.82 | 2/9 | 1.22 |
| 80.00 | 1/4 | 1.25 |
| 77.78 | 2/7 | 1.29 |
| 76.92 | 3/10 | 1.3 |
| 75.00 | 1/3 | 1.33 |
| 73.33 | 4/11 | 1.36 |
| 71.43 | 2/5 | 1.4 |
| 69.23 | 4/9 | 1.44 |
| 66.67 | 1/2 | 1.5 |
| 65.22 | 8/15 | 1.53 |
| 63.64 | 4/7 | 1.57 |
| 61.90 | 8/13 | 1.62 |
| 60.00 | 4/6 | 1.67 |
| 57.89 | 8/11 | 1.73 |
| 55.56 | 4/5 | 1.8 |
| 52.38 | 10/11 | 1.91 |
| 50.00 | 1/1 | 2 |
| %age | Fractional Odds | Decimal Odds |
|---|---|---|
| 50.00 | 1/1 | 2 |
| 47.62 | 11/10 | 2.1 |
| 44.44 | 5/4 | 2.25 |
| 42.11 | 11/8 | 2.38 |
| 40.00 | 6/4 | 2.5 |
| 38.10 | 13/8 | 2.63 |
| 36.36 | 7/4 | 2.75 |
| 34.78 | 15/8 | 2.88 |
| 33.33 | 2/1 | 3 |
| 30.77 | 9/4 | 3.25 |
| 28.67 | 5/2 | 3.5 |
| 26.67 | 11/4 | 3.75 |
| 25.00 | 3/1 | 4 |
| 23.08 | 10/3 | 4.33 |
| 22.22 | 7/2 | 4.5 |
| 20.00 | 4/1 | 5 |
| 18.18 | 9/2 | 5.5 |
| 16.67 | 5/1 | 6 |
| 15.39 | 11/2 | 6.5 |
| 14.29 | 6/1 | 7 |
| 12.50 | 7/1 | 8 |
| 11.11 | 8/1 | 9 |
| 9.09 | 10/1 | 11 |
| 7.69 | 12/1 | 13 |
| 5.88 | 16/1 | 17 |
| 4.76 | 20/1 | 21 |
| 3.85 | 25/1 | 26 |
| 2.94 | 33/1 | 34 |
| 1.96 | 50/1 | 51 |
| 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.