3. Implied probability

Odds → probability and back

Odds do not only tell you how much a bet pays. They also carry how likely it is to come in according to the bookmaker’s price. This chance, read back out of the price, is what we call the implied probability. The most important formula of the course fits on one line: implied probability = 1 / decimal odds (decimal odds are the multiplier format, for example 2.00). 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. Keep one thing in mind: this percentage also contains the bookmaker’s profit, so it is a little higher than the true chance. How much higher is what the next section looks at.

Why exactly 1/odds? Because it is the break-even point: the hit rate at which you neither win nor lose. Decimal odds show the total return, your stake included: a €10 stake at odds of 2.50 pays back €25. So if you place ten bets of €10, €100 in total, and four of them win, exactly 4 × €25 = €100 comes back: you are at zero. If the true chance is above 40%, you win in the long run; if below, you lose. Nobody knows the true chance exactly, of course, it can only be estimated, and much of the course is about that. And the long run here means several hundred bets: over ten or twenty tips luck overrides everything. 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

A market here is all the possible outcomes belonging to one question. The best known is the 1X2 market: home win (1), draw (X), away win (2). Exactly one of these happens at the end of the match, so the three true chances have to add up to exactly 100%. Yet 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%. This does not mean that the chance is 104.8% in reality, a probability can be 100% at most. The excess is the bookmaker’s margin (also called overround, or vig in betting slang, and shown as margin on the platform too): 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, that is, without the bookmaker’s profit. Fair here does not mean that this price is owed to you, nor that you can bet at it anywhere: it is a reference point calculated on paper. The simplest is the proportional method: divide each implied probability by the sum, which takes the surcharge out of every outcome in the same proportion. In the example the home side is 47.6 / 104.8 = 45.4%, and since odds = 1 / probability, that gives 1/0.454 = 2.20: the fair odds are 2.20 instead of the offered 2.10, and the difference is the bookmaker’s profit on this outcome. 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 is measured against the fair probability, not against the offered odds. Value (chapters 10-11) is one: whether the price you got is better than the true chance would justify. CLV (chapter 12) is another, the edge measured against the closing price: whether you bet at a better price than the one that had formed by kick-off. And so is the evaluation of models (Module VI). In chapter 15 you will see that the fair prices of sharp bookmakers are the best publicly available estimates of the true chance. A sharp bookmaker is one that works with a small margin, adjusts its prices quickly and accepts large stakes too. 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

Five short exercises, the calculator on your phone is enough for all of them. 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: first turn the 30% into a decimal (30% = 0.30), and only then divide: 1/0.30 = 3.33. If you type 1/30, you get 0.033, and that is not an odds.
• 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%, and that is the bookmaker’s margin on this market (the exact calculation is in chapter 4).
• 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, meaning that every €100 staked returns €112.50 on average, that is a profit of +12.5% (the formula is in chapter 10).
• 5A three-leg multiple (a leg is one tip on the slip, and all three have to be right, otherwise the whole thing loses): 1.80, 2.00, 2.20. In a multiple the odds are multiplied together, because the winnings are rolled on. What combined chance is needed to break even? Solution: 1 / (1.80 × 2.00 × 2.20) = 1/7.92 = 12.6%, so roughly one time in eight all three have to come in.

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.