3. Implied probability

Odds → probability and back

The most important formula of the course fits on one line: implied probability = 1 / decimal odds. So 2.00 says 50%, 1.25 says 80%, 5.00 says 20%. When the bookmaker gives a price, it is really conveying a probability, just in the language of money. From this point on, look at every odds as a percentage.

Why exactly 1/odds? Because it is the break-even point. If you bet at odds of 2.50, you need to win four times out of ten to break even: 4 × 2.50 = 10 units of payout on 10 units of stake. If the true chance is above 40%, you win in the long run; if below, you lose. So 1/odds also tells you the hit rate above which the given price is worth it.

The same way back: odds = 1 / probability. If you put the chance of an outcome at 25%, the corresponding price is 4.00. A few anchor points worth knowing by heart:

The odds are not a prophecy or a mood: they are a numerical statement about the chance. Whoever sees odds and not a percentage is still thinking in the bookmaker’s language, not their own.

The concept of fair odds

If you add up the implied probabilities of a whole market, an unpleasant surprise awaits: the sum is always more than 100%. On a typical 1X2 market (2.10 / 3.40 / 3.60) the implied probabilities are 47.6%, 29.4% and 27.8%, a total of 104.8%. The excess is the bookmaker’s margin: this is how much more expensively you buy the probability than it is worth.

Fair odds are the price you would get after removing the margin. The simplest, proportional method: divide each implied probability by the sum. In the example the home side is 47.6 / 104.8 = 45.4%, so the fair odds are 2.20 instead of the offered 2.10. The more precise methods and the margin calculation are worked through in chapter 4, and the platform’s margin calculator computes it with a single click (chapter 43).

Why is this so important? Because every later concept of the course — value (chapters 10–11), CLV (chapter 12), the evaluation of models (Module VI) — is measured against the fair probability. In chapter 15 you will see that the fair prices of sharp bookmakers are the best publicly available estimates, and the platform’s Pro odds page computes exactly such fair prices (chapter 42).

The offered odds always mix two things: the market’s estimate of the chance and the bookmaker’s margin. The fair odds are the separation of the two. Without this you cannot judge whether you are getting a good price.

Calculation exercises with real odds

Practice exercises: first calculate, only then check the solution.

• 1What is the implied probability of odds of 1.85? Solution: 1/1.85 = 54.1%.
• 2You estimate the chance of an outcome at 30%. What are the fair odds? Solution: 1/0.30 = 3.33.
• 3A two-outcome market, both sides 1.90. What is the total implied probability? Solution: 52.6% + 52.6% = 105.3%, the excess is 5.3%.
• 4You bet at odds of 2.50, with a 45% hit rate in the long run. Are you profitable? Solution: break-even is 40%, so yes: 0.45 × 2.50 = 1.125, i.e. +12.5% (the formula is in chapter 10).
• 5A three-leg multiple: 1.80, 2.00, 2.20. What combined chance is needed to break even? Solution: 1 / (1.80 × 2.00 × 2.20) = 1/7.92 = 12.6%.

From here on we read every odds as a probability. The end-of-chapter test practises with new values on every attempt, and in real use the platform’s calculators (chapter 43) give the same with a single click.