**The maths behind odds and gambling can help determine whether a wager is worth pursuing and that's an incredibly valuable tool to have at your disposal. **

The first thing to understand is that there are three distinct types of odds: factional, decimal, and American (money line). The various types represent different formats to present probabilities, which are also used by bookmakers, and one type can be converted into another. Once the implied probability for an outcome is known, decisions can be made regarding whether or not to place a bet or wager.

## ♻️ Converting Odds to Implied Probabilities

Although odds require complicated calculations, the concept is easier to understand once you fully grasp the three types of odds and how to convert the numbers into implied probabilities.

- Fractional odds are sometimes called British odds or traditional odds and are sometimes written as a fraction, such as 6/1, or expressed as a ratio, like six-to-one.
- Decimal odds represents the amount that is won for every $1 that is wagered. For instance, if the odds are 3.00 that a certain horse wins, the payout is $300 for every $100 wagered.
- American odds are sometimes called money line odds and are accompanied by a plus (+) or minus (-) sign, with the plus sign assigned to the lower probability event with the higher payout.

Here are some simple, methodical steps via **Investopedia**:

There are tools available to make conversions between the three types of odds. Many online betting websites offer an option to display the odds in the preferred format. The table below can help convert odds with pen and paper, for those interested in doing the calculations by hand. Here's a handy table that shows you your chance of winning bets at multiple odds levels:

Converting odds to their implied probabilities is perhaps the most interesting part. The general rule for the conversion of (any type of) odds into an implied probability can be expressed as a formula:

**** Implied Probability Of An Outcome = stake divided by total payout **

As shown, the formula divides the stake (amount wagered) by the total payout to get the implied probability of an outcome. For example, a bookmaker has the (fractional) odds of Man City defeating Crystal Palace at 8/13. Plug the numbers into the formula, which is a simple matter of dividing 8 by 13 in this example, and the implied probability equals 61.5%. The higher the number, the greater the probability of the outcome.

Using an example of decimal odds, a candidate has 2.20 odds to win the next election. If so, the implied probability is 45.45%, or 1/2.2 * 100.

*📊 The bottom line*

A betting opportunity should be considered valuable if the probability assessed for an outcome is higher than the implied probability estimated by the bookmaker. Furthermore, the odds on display never reflect the true probability of an event occurring (or not occurring). The payoff on a win is always less than what one should have received if the odds had reflected the true chances. This is because the bookmaker’s profit margin is included in the odds.

*🍔 Key takeaways*

- The three types of odds are fractional, decimal, and American.
- One type of odd can be converted into another and can also be expressed as an implied probability percentage.
- A key to assessing an interesting opportunity is to determine if the probability is higher than the implied probability reflected in the odds.
- The house always wins because the bookmaker's profit margin is also factored into the odds.

📲 Catch up on our article covering **value & introducing implied probability** in case you missed it!