Probability is a branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring. In pure chance games, each instance is completely independent; each play has the same probability of producing a given outcome as the others. In practice, probability statements apply to a long series of events but not to individual circumstances. Probability (p) equals the total number of favorable outcomes (f) divided by the total number of possibilities (t), or p = f/t. This is true only in situations governed solely by chance. Are you still with us? Good! Let’s slow things down and take it from the top.

Gamblers and astronomers — two very different groups of people — were responsible for developing probability theory. The former desired a better understanding of slot machine results and odds, while the latter desired accurate observations from their rudimentary tools. Then, around the 16th century, mathematicians made connections between gambling and probabilities. They explored the concept of permutation in gambling to discover various theories. Probability theory is now the foundation of many other scientific fields, including finance, insurance, weather forecasting, resource planning, epidemic preparedness, and predicting how people will vote in an upcoming election. Even the most advanced physics theory, quantum theory, uses probability distributions to describe the motion of particles on a microscopic scale.

By definition, all probabilities are fractions. However, several ways to express a fraction can be used to calculate a percentage of a likely event. For example, assume you have a two-headed coin. What is the likelihood of the coin landing on heads? And what is the possibility that it will land on tails? Because there are two heads, you have a 100% chance of getting a heads result and a 0% chance of getting a tails result.

Let’s look at poker as another example, which is slightly more complex. Anyone who knows anything about poker understands that you have just as much chance of hitting four-of-a-kind as the person sitting next to you. After all, you’re both drawing from the same 52-card deck. What you do with those cards after that is essential. Assume you’re playing a five-card draw, and you’re dealt a hand with four cards to a flush. You’re going to discard a card, hoping to draw a flush. What is the likelihood that you will succeed?

The deck is down to 47 cards. Nine of them are the suit you require, so your chances of getting the card you need are 9/47, or 19.1%. That’s nearly one in every five or 20%. If you assume you must win the pot with this hand, you can calculate how much money needs to be in the pot to profitably call a bet. This is referred to as the expected value (EV). The sum of all possible probabilities multiplied by their associated gains or losses yields the expected value. Its concept is significant because it indicates how much money you can expect to earn.

Man has been looking for ways to beat the system since the invention of gambling games or games of chance. So it’s no surprise that the great minds of history have become immersed in gambling theory, especially if they were gamblers themselves. Since the Enlightenment, many mathematicians have been busy developing new and improved ideas to help gamblers. It’s no surprise that many people seek an advantage when playing gambling games. To that extent, they have attempted to test various game probabilities using mathematics. A school of thought in gambling theory holds that knowing probability will give you an advantage.

Understanding how to calculate implied probability from betting odds is essential for determining potential value in a betting market. Furthermore, knowing how to convert betting odds into implied probabilities is critical for betting because it enables you to assess the potential value of a market. If the implied probability is less than your assessment after conversion, it represents betting value. Therefore, we can conclude that knowing how to calculate and assess probability can help you win when gambling. Well…it probably can!