Probabilities versus Odds: Calculating the Outcomes of an Event – The Ubiquitous Coin Toss Challenge

Are you interested in determining the outcome of an event like an English Premier League football match before the game starts? Is it even possible to use probabilities to work out which team has the greatest chance of winning the game? Why would you need to calculate the possible outcomes of an event before it starts?

These questions are valid and deserve considered answers.

Before we answer them by looking at the following points, the concise answer to the question of whether you can use probabilities and odds to calculate the outcome of an event before it starts is: Yes, you can.

And the answer to why you would need this knowledge is that many casino activities like betting on the outcome of a football match, are based on calculated odds and probabilities. Therefore, you will increase your odds of winning if you study which team is likely to win before placing any bets.

Probability versus Odds: What’s the difference?

Even though these terms are often used interchangeably, there is a marked difference between the two.

Keith McNulty notes in his article titled, “Are you mixing up odds with probability?” that both terms “imply an estimate of chance.” Even though these terms are related concepts, they are notably different in “scale and meaning.”

McNulty goes on to state a “probability is defined as the number of occurrences of a specific event expressed as a proportion of all events that could occur.”

Juxtapositionally, the odds of an event occurring are described as the number of occurrences of an individual event represented as a proportion of the number of non-occurrences of the same event.

Probability versus Odds: A case study

While the definitions of these terms can overcomplicate matters, the best way to describe them in action is to look at the coin toss challenge. It provides the perfect setting for an explanation of the difference between these two statistical terms because there will only ever be one of two outcomes: heads or tails facing the top when the coin lands after being tossed.

Let’s assume that you involved in a friendly coin toss challenge and you which to know what your odds are choosing the correct option.


Because there are only two options, heads or tails. The probability of either event occurring is 50% or 1/2.  There is a 50% chance that when flipped, the coin will land heads up or it will land tails up. These outcomes are mutually exclusive.

The calculation used to determine the probability of either event occurring is:

Number of outcomes in the event divided by the total number of possible outcomes.

The number of outcomes in the event is 1 and the total number of possible outcomes is 2.

Therefore, the probability of either event occurring is 1/2.


The odds of one of the two events occurring is 1:2. This number is represented as a ratio and simply means that there will one of the two possible outcomes.

In other words, there can only be 1 outcome at a time. Every time the coin is flipped, it will either land heads up or tails up.

The maximum number of outcomes will always be 2. Therefore, the odds of the coin landing heads up or landing tails up when tossed is 1:2.

John Norwood
John Norwood is best known as a technology journalist, currently at Ziddu where he focuses on tech startups, companies, and products.