Odds and Probability

Sports betting is rooted in mathematics and the main job for a bookmaker in constructing any market is working out the different probabilities of all possible outcomes, so that they can set their odds accordingly to try and make a profit, whilst making sure the prices are fair enough to attract punters and reward those who have good powers of prediction.

Probability is calculated by a simple formula which divides the chances of one potential outcome by the total number of possible outcomes. For example, a standard coin can either land heads-up or tails-up and there is an equal chance of both outcomes. The probability of tossing both a head and a tail is 1 in 2, which may be referred to as a percentage (50) or a number between 0 and 1 (0.5), where an impossible outcome is 0 and a certain one is 1.

In terms of statistics, odds work in a similar way and are displayed as the chances of an outcome happening versus the odds against the same outcome occurring. Gambling odds represent the stake which a punter must put down to win a bet and are based on the bookmakers’ best estimation of the likelihood for certain events to take place.

One key difference, however, is that whereas the total number of possible outcomes equals 100 percent in probability, for example a 50 percent chance of spinning a coin to land on heads and a 50 percent chance of spinning a coin to land on tails, the odds on any betting market will always add up to more than 100 percent.


A rugby union match has odds of 5/6 that the total amount of points will be an even number, and there is also a price of 5/6 that the total amount of points will be an odd number.

  • Odds of 5/6 equate to the bookie giving the match a 54.54 percent chance of finishing with an even number of points scored, and the same for odd.
  • This is calculated by dividing the second number by the total of the two numbers, before multiplying by 100 to get a percentage (6 divided by 11, multiplied by 100, as bettors have to pay £6 to win £5, for a return of £11).
  • 54.54 + 54.54 = 109.09

A Premier League football match has odds of 6/5 on Manchester United to beat Manchester City, 11/5 on a Man City win and 12/5 on a draw.

  • Odds of 6/5 equate to the bookie giving Man Utd a 45.45 percent chance of winning (i.e. that they will win 5 times out of 11, and not win 6 times out of 11).
  • Odds of 11/5 equate to the bookie giving Man City a 31.25 percent chance of winning (i.e. that they will win 5 times out of 16, and not win 11 times out of 16).
  • Odds of 12/5 equate to the bookie giving the match a 29.41 percent chance of ending in a draw (i.e. that 5 out of 17 matches will end in a draw, and 12 out of 17 won’t).
  • 45.45 + 31.25 + 29.41 = 106.11

Ensuring that odds add up to just over 100 percent but setting them at the right price to try and attract as many wagers as possible on each outcome is really the essence of a bookmaker’s job, and the skill for sports bettors is found in trying to judge where the values have been pitched somewhat incorrectly. Visit the value bets page to learn how customers can spot these opportunities.

You can use the following table to see how various odds reflect the implied probability of outcomes happening.

Odds Implied Probability
1/100 99%
1/50 98%
1/10 90.9%
1/3 75%
2/5 71.41%
Evens 50%
5/2 28.57%
3/1 25%
10/1 9.09%
50/1 1.96%
100/1 1%

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