Sports Betting is Pure Mathematics - Learn the Simply Formula Behind Betting Odds and Win More

 

The math underlying odds and gambling can help determine whether a wager is worth pursuing. 

The first thing to understand is that there are three distinct types of odds: fractional, decimal, and American (moneyline). 

The various types are 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.

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.

Converting Odds to Implied Probabilities

Although odds require seemingly complicated calculations, the concept is simple 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 moneyline odds and are accompanied by a plus (+) or minus (-) sign, with the plus sign assigned to the lower probability event with the higher payout.

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.

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:

Rule:

\begin{aligned} &\text{Implied Probability Of An Outcome} = \frac{ \text{Stake} }{ \text{Total Payout} } \\ &\textbf{where:} \\ &\text{Stake} = \text{Amount wagered} \\ \end{aligned} 

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Implied Probability Of An Outcome= 

Total Payout

Stake=Amount wagered

​

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. 

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