Calculating Betting Odds

Now that we know the probability, let’s look at the odds being offered on this bet. For some reason, the odds for heads are set at -300, while tails are +260. This would be a very odd occurrence for such a bet but bear with me. Now we must calculate the implied probability of both lines being offered and determine which bet contains the most value.

First, we will solve the implied probability for heads. I find it easiest to convert the moneyline value to decimal odds before converting to a percentage:

(100/-300) + 1 = 1.33

Now we take our decimal odds and convert them to a percentage:

Now we will solve for tails:

(260/100) + 1 = 3.6

1/3.6 = 0.2778

0.2778 X 100 = 27.78 %

In this instance, the probability of tails landing far outweighs the implied probability determined by the odds being offered. This is a high-value bet.

Calculating the real probability and comparing that number to the implied probability set by the odds is the primary strategy with which one should approach every bet.

Decimal

Decimal odds are the favorite way to express betting lines in Europe. They are the most straightforward method of communicating odds. The decimal value is the amount that will be returned per each dollar bet. What makes this system particularly helpful is that both the amount staked and the winnings are included.

So let’s say we made a $10 bet at 3.5 odds. Our total return for winning that wager would be $35. $25 is the profit, with the other $10 being the return of our stake.

Fractional

Fractional odds are most commonly found at racetracks or for futures bets when there are entire pools of participants that can possibly win. This format expresses odds in the form of fractions such as 4/1, which would be pronounced “four-to-one.” Four-to-one odds means that you will earn $4 for every $1 that you stake.

Sometimes the fractions will be less straightforward. You may see numbers like 9/2, for example. To calculate the return on a 9/2 bet, let’s pretend that we bet $20 at 9/2 odds for a horse race.

[Amount staked X (numerator/ denominator)] + Amount staked

Moneyline/American

The moneyline system of presenting odds utilizes negative and positive three-digit values to represent which bets are favored or underdogs. A positive number means that a play is considered the underdog. The quantity after the “+” is the amount that will be won for every $100 bet.

On the other end of the spectrum, favorites are displayed with a negative value such as -350. This means that you must bet $350 to win $100. Moneyline odds only calculate the amount potentially won on a bet, and not the total payout.

To learn how to calculate odds, let’s make things a bit more interesting with a switch from a coin toss to a roll of a six-sided die. The wager that we are making is that the die will land on 3. In this example, we are looking at one desired outcome. If there are six possible outcomes on a roll of the die, and only one outcome is desirable, that means there are five undesirable results.

Now we can calculate the odds against us winning, as well as the odds in favor of a win. To calculate the odds in favor, simply divide the one possible desired outcome by the total outcomes possible.

1/6 = 0.1667

5/6 = 0.833

0.833 X 100 = 83.3 % chance of losing our bet.

You may want to calculate an odds ratio based on a particular probability. In order to solve this equation, we will need to express the probability as a fraction. Using the same six-sided die from before, the possibility of our number landing formatted as a fraction is 1/6.

Next, just subtract the numerator from the denominator:

To solve for probability given an odds ratio, we merely reverse the equation. First, we put our odds ratio in fraction form:

1/6 probability = 1:5 odds

There are numerous odds calculators available online that are probably faster to use, but it’s still best that you understand the formulas for converting different odds types to other formats. Below are all of the equations required to transform any kind of odds to any other arrangement.

The odds always stay the same; they are just represented differently. At times, being able to convert formats can be extremely helpful, especially when switching to decimals when solving for implied probability.

Moneyline to Decimal

To convert positive moneyline odds, the equation is:

(Moneyline odds/100) + 1 = Decimal odds

To convert negative moneyline odds, the equation is:

(100/Moneyline odds) + 1 = Decimal odds

Moneyline to Fractional

To convert positive moneyline odds, the equation is:

(Moneyline odds/100) = Fractional Odds

To convert negative moneyline odds, the equation is:

-100/Moneyline odds = Fractional Odds

Fractional to Decimal

(Numerator/Denominator) + 1 = decimal odds

Fractional to Moneyline

(Numerator/Denominator)

If the result is greater than or equal to 1:

100 X (Answer) = Moneyline odds

If the result is less than 1:

-100/(Answer) = Moneyline odds

Decimal to Fractional

Decimal odds – 1 = X

Put X over 1

Example:

• 3.5 – 1 = 2.5
• 2.5/1 = 5/2
• 3.5 decimal odds = 5/2 fractional

Decimal to Moneyline

If decimal odds are greater than 2:

100 X (decimal odds – 1) = Moneyline odds

If decimal odds are less than 2:

-100/(decimal odds -1) = Moneyline odds

Finding implied probability from decimal odds is extremely easy. Let’s say the decimal odds are 2.5.

• 1/2.5 = 0.4
• 0.4 X 100 = 40% Implied Probability

From Moneyline Odds

Calculating implied probability for a -150 favored moneyline bet:

• (- (-150)/((-(-150)) + 100 =
• 150/(150 + 100) = 150/250 = 0.6
• 0.6 X 100 = 60% Implied Probability

Calculating implied probability for an +250 underdog moneyline bet:

• 100/(250 + 100)
• 100/350 = 0.2857
• 0.2857 X 100 = 28.57% Implied Probability

From Fractional Odds

Denominator/(denominator + numerator) X 100

• Calculate the implied probability of 15/2 odds.
• 2/(2 + 15) X 100 = 2/17 X 100 =
• 0.12 X 100 = 12 % Implied Probability