How to Calculate Probability from Betting Odds

The majority of people think that probability just means that something will probably happen. While this is true in certain cases, it is far from true in every situation and for every event. There are truly precise scientific ways to calculate the likelihood of an outcome occurring and for each type of event those methods produce very different results. This article is going to shed some light on probability, how it is calculated and how it can vary. Let’s get started.

Probability Treats Events As Independent Ones

One of the fundamental things that you need to understand about probability is that events are not necessarily independent. For example, if you throw a coin and it comes up heads ten times in a row, the chances of that continuing are very slim. But wait just a minute, did you just say that the chances of tails coming up ten times in a row is slim? That is correct, and it can be calculated as such:

(1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) = 0.0005

What this means is that if you are betting on heads or tails in a coin toss, you should not assume that the individual tosses are independent of each other. For example, if you toss a coin and it comes up heads three times in a row, that does not mean that you will necessarily get three heads in the next four tosses. This is because there is still a 1/8 chance that the next toss will be tails and that too would be a catastrophic result for your wagering purposes. Or if you are dealing with a craps game with odds of 19 to 1, that means that there is a 1/19 chance that the next spin will result in a 7 or an 11. You have to take that into consideration when using that type of probability.

The Law of Total Probability

One of the most important concepts in probability is that of total probability. Total probability is a bit like the opposite of independence, which you must remember is not the same as interdependence. For example, if you have a coin that is already heads up, what is the chance that it will come up tails on the next toss? That is very unlikely to happen, and hence the probability is small (though still conceivable). But what if the coin is already tails up, does that change anything? Well, that is an interdependent probability and it means that if you already know that the coin is tails up, the chances of it coming up tails on the next toss is increased. This is a very important concept to understand about probability because it can change how you think about individual events:

Since total probability is the combination of the independent probabilities of each event, you can multiply the probabilities together to find the overall chance of an outcome:

1/2 x 1/2 x 1/2 x 1/2 = 0.01

This method is often called the multiplication rule and it is used whenever one or more probabilities are multiplied to find the overall chance of an event.

Odds Are A Measure Of Likelihood

Another important concept to understand about probability is that of odds. Odds are a way of quantifying the likelihood of an event occurring. For example, if you are playing craps and the house odds are 18 to 1 (and you are currently short), that means that if you roll a 7, you will win $18. But if you roll an 11, you lose everything. So basically, the chances of you winning or losing are equal since the house odds are exactly what you would have to beat to win your bet (in this case, $1). This is why odds are often used to measure the likelihood of an event occurring. The chance of winning is equal to the odds of winning multiplied by the amount you are wagering (in this case, $1). As a general rule, the higher the house odds, the greater the likelihood of an event occurring:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.125

Similarly, if the house odds are 37 to 1, the chances of winning are only 1/37, which is far more manageable. That is because a 37-to-1 chance of winning is a lot more likely than an 18-to-1 chance of winning. But again, this is all relative.

Probability Never Stands Still

Finally, it is important to understand that probability can never stand still. That is because as things change, so does probability and its calculations change with it. Let’s say that you have a coin and it comes up heads ten times in a row. Suddenly, it starts coming up tails and your old calculation of heads ten times in a row is no longer correct. Instead, you need to use a new formula that takes the latest turn of events into consideration.

Say you just witnessed ten consecutive tails in the most recent spin of the coin. That means that the probability of getting ten tails in a row in the next spin is now 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x (1/2) x 1/2 x (1/2) x 1/2 x (1/2) x (1/2) x (1/2) = 0.25. This change occurs because the latest events have altered the chance of getting the previous event (in this case, heads). While it is easy to calculate the probability of getting ten tails in a row when that is your only outcome (this is just a simple application of the multiplication rule), it can be tricky to determine the odds of a specific event occurring given all the different possibilities presented by the latest turn of events. This is why probability is always a moving target and it is not something to simply add up because the latest events happened. Instead, you need to calculate the probability in light of all the new information. This can be challenging and it can lead to some very interesting situations, which you can also use for your advantage when betting. So keep this in mind when utilizing probability in your wagering activities.