🎓 Lesson 3: Odds as Probability

🎯 Objective

By the end of this lesson, you will:

• Understand the relationship between odds and probability.
• Be able to convert from odds to probability.
• Be able to convert from probability to odds.

🧭 Introduction

                 Earlier, you learned that odds can be seen as a representation of probability. If you’ve never studied probability before, don’t worry, you don’t need advanced math to understand this relationship. What matters is grasping the basic idea of what probability means in simple, practical terms.

🙋‍♂️ What Is Probability?

                 If you’ve done some mathematics, the word “probability” might sound intimidating. If you haven’t, it may just feel like a normal word and that’s exactly how you should see it.

Probability is simply a measure of how likely an outcome is to occur.
It is always expressed as a number between 0 and 1 or as a percentage between 0% and 100%.

Other everyday words for probability include:

• 🔹 Chance
• 🔹 Likelihood
• 🔹 Possibility

Essentially, probability turns these abstract ideas into numbers so we can work with them.
This is useful in sports betting because you’ll deal with lots of numbers and need to manipulate them to make decisions.

🧮 Examples

What is the chance that Portugal wins the next FIFA World Cup?

• You might say 30%. That’s your estimate of the probability, in this case 0.3 or 30%.

What is the likelihood of getting heads on a coin toss?

• That’s a 50% chance. Half for heads, Half for tails or 0.5 probability for each.

🚨 Notice how it’s easy to state the probability for a coin toss, but much harder for Portugal winning the World Cup. That’s because some probabilities are exact (like coin flips), while others must be estimated.

💡 Key Point:

For any outcome, there is one true probability, it exists and it’s unique.

If two people have different probabilities for the same event, at least one is wrong. In sports betting, your goal is to estimate that true probability as closely as possible.

🔁 Relationship Between Odds and Probability

Odds and probability are closely related. In sports betting you can easily convert between them:

• The decimal odds of an outcome = 1 ÷ Probability of that outcome
• Probability of an outcome = 1 ÷ The decimal odds of that outcome

❗️ Important Notes

When using the above formulas

• Probability must be a number between 0 and 1 (not 0%–100%).
• Odds must be a number ≥ 1.

Each time you see an outcome, you can now quickly calculate its chance of occurring and vice versa.

🧮 Example 1 - Stake

Below is a Both Teams to Score market on Stake:

• Event: Chelsea FC vs Liverpool FC
• Tournament: English Premier League
• Kick-off: 10/04/2025, 5:30 PM (GMT+1)

In this market there are 2 outcomes:

• Both teams to score – Yes
• Both teams to score – No

The odds for each outcome are:

• Yes: 1.51
• No: 2.50

Using the formula Probability = 1 ÷ Odds, the implied probabilities are:

• Yes: 1 ÷ 1.51 = 0.6623 → 66.23% chance
• No: 1 ÷ 2.50 = 0.40 → 40% chance

Interpretation

• For the outcome Both teams to score - Yes, Stake believes there’s a 66.23% chance that both teams will score.
• For the outcome Both teams to score - Yes, Stake believes there’s a 40% chance that both teams will not score.

💡 Note

These are Stake’s implied probabilities, not absolute truths.
You can have your own estimate and often, different bookmakers will have slightly different numbers.

🧮 Example 2 - Pinnacle

Let’s check the same market on Pinnacle:

The odds for each outcome are:

• Yes: 1.502
• No: 2.68

Using the formula Probability = 1 ÷ Odds, the implied probabilities are:

• Yes: 1 ÷ 1.502 = 0.6658 → 66.58%
• No: 1 ÷ 2.68 = 0.3731 → 37.31%

Interpretation

• Pinnacle believes there’s a 66.58% chance that both teams will score.
• Pinnacle believes there’s a 37.31% chance that both teams will not score.

🚨 Notice

Pinnacle’s view differs slightly from Stake’s.
Each bookmaker has its own model and risk tolerance, so implied probabilities vary.

🧩 Why This Matters

                 If multiple people (or bookmakers) disagree on a probability, who’s correct?. Remember there is only one true probability, and differences between bookmakers can signal opportunity. This concept is the foundation of value betting, which you’ll explore later.

                 If you’d rather not do the math manually, use the 🔗 free odds to probability calculator on OddsFantasy

🚀 Call To Action

Take a moment to open your bookmaker account and look at a few markets.
Pick some outcomes and calculate their probabilities using the calculator.

Every successful punter understands how odds and probability are connected and how to convert between them.

🤓 Curious why Decimal Odds = 1 ÷ Probability?

                 The proof requires knowledge in advanced probability and statistics (outside the scope of this lesson). For now, just focus on using the formula confidently.

🔁 Recap

• Probability measures how likely an outcome is (0 to 1 or 0% to 100%).
• You can convert between odds and probability using: Probability = 1 ÷ Odds
• Each bookmaker’s odds represent their opinion, but there’s always one true probability.
• Practising conversions on real markets makes them second nature.

🔮 Next Chapter Preview

In the next lesson, you’ll look at odds as a price. You’ll learn how to:

• Calculate potential payouts if your bet wins,
• Compare returns across different bets.

⏭️ Next