What Is Implied Probability in Betting?
Implied probability is the chance of an outcome that the betting odds suggest. To find it, divide 1 by the decimal odds and multiply by 100. Odds of 2.50 give 1 ÷ 2.50 × 100 = 40%.
Implied probability example: Enyimba vs Rivers United
Here is a 1X2 market. "1X2" means home win (1), draw (X) or away win (2).
| Outcome | Odds (example odds) | Working | Implied probability |
|---|---|---|---|
| Enyimba win (1) | 2.20 | 1 ÷ 2.20 × 100 | 45.45% |
| Draw (X) | 3.10 | 1 ÷ 3.10 × 100 | 32.26% |
| Rivers United win (2) | 3.40 | 1 ÷ 3.40 × 100 | 29.41% |
The odds suggest Enyimba wins about 45 times in 100. They suggest a draw about 32 times in 100.
Say you stake (the money you bet) ₦1,000 on Enyimba at 2.20. If the match ends 2–1 to Enyimba, you get ₦1,000 × 2.20 = ₦2,200. That is ₦1,200 profit plus your stake back.
What is the implied probability formula?
The implied probability formula is 1 ÷ decimal odds × 100. The answer is a percentage.
- Implied probability = 1 ÷ odds × 100
Example: odds of 4.00 give 1 ÷ 4.00 = 0.25. Multiply by 100 and you get 25%.
You can also go the other way. To turn a percentage into odds, divide 100 by the percentage. So 25% becomes 100 ÷ 25 = 4.00.
If your bookmaker shows fractional odds, such as 5/2, convert them to decimal first. Our guide on how betting odds work shows how.
How do you convert odds to percent?
You convert odds to percent with the same formula: divide 1 by the odds, then multiply by 100. This table shows common odds.
| Decimal odds | Implied probability | Roughly |
|---|---|---|
| 1.25 | 80.00% | 4 times in 5 |
| 1.50 | 66.67% | 2 times in 3 |
| 1.80 | 55.56% | a bit over half |
| 2.00 | 50.00% | 1 time in 2 |
| 2.50 | 40.00% | 2 times in 5 |
| 3.00 | 33.33% | 1 time in 3 |
| 4.00 | 25.00% | 1 time in 4 |
| 5.00 | 20.00% | 1 time in 5 |
| 10.00 | 10.00% | 1 time in 10 |
Lower odds mean a higher implied probability. Higher odds mean a lower one. Even at 1.25, the odds suggest the outcome fails about 1 time in 5.
What is bookmaker margin, or overround?
Bookmaker margin is the extra the bookmaker builds into the odds so it profits over time. It is also called the overround. You can see it by adding up all the implied probabilities in one market.
Use the Enyimba example:
45.45% + 32.26% + 29.41% = 107.12%
Only one of the three results can happen. So in a fair market, the three chances would add up to exactly 100 percent. Here they add up to 107.12%. The extra 7.12% is the margin.
The margin makes every price a little lower than the fair price. You can remove it to estimate fair odds. Divide each implied probability by 107.12, then multiply by 100.
| Outcome | Bookmaker odds | Without margin | Fair odds |
|---|---|---|---|
| Enyimba win | 2.20 | 42.43% | 2.36 |
| Draw | 3.10 | 30.11% | 3.32 |
| Rivers United win | 3.40 | 27.46% | 3.64 |
The fair percentages now add up to 100 percent. This method is a simple estimate. Bookmakers may not spread the margin evenly.
Because of the margin, most bettors lose money over time. A smaller margin means slightly better odds for you.
Why does your own estimate matter?
Your own estimate matters because implied probability is only the bookmaker's view. It is not a fact. To judge a bet, you compare the implied probability with your own estimate of the chance.
Say you think Enyimba wins about 50% of the time. The odds of 2.20 suggest only 45.45%. If your estimate is right, the price is higher than it should be. This is called a value bet.
Now say you think Enyimba wins only 40% of the time. Then 2.20 is a poor price for you, even if Enyimba is the favourite.
Be honest with yourself here. Your estimate can be wrong. Bookmakers use a lot of data, so beating their prices is hard.
How does implied probability work for accumulators?
For an accumulator, you multiply the odds, and the implied probability is 1 ÷ the total odds × 100. An accumulator (one bet that joins several picks) wins only if every pick wins.
Take three picks at 1.50, 1.80 and 2.00:
- Total odds: 1.50 × 1.80 × 2.00 = 5.40
- Implied probability: 1 ÷ 5.40 × 100 = 18.52%
You get the same answer if you multiply the single probabilities. That is 66.67% × 55.56% × 50.00% = 18.52%.
Each pick looks fairly likely on its own. Together, the odds suggest the bet wins less than 1 time in 5. A ₦1,000 stake would return ₦1,000 × 5.40 = ₦5,400 if all three win. Check your own slips with the payout calculator.
The margin also stacks. Each pick carries its own margin, so long accumulators carry a large total margin.
Common mistakes
- Treating implied probability as the real chance. It is the bookmaker's estimate, and it includes the margin.
- Forgetting the margin. The percentages in one market add up to more than 100 percent, never exactly to it.
- Adding accumulator chances. You must multiply them. Three 50% picks give 12.50%, not 150%.
- Thinking low odds are safe. Odds of 1.25 still suggest a loss about 1 time in 5.
- Trusting your estimate too much. Your own number can be wrong, so test it over many bets.
FAQ
Is implied probability the real chance of a result?
No. It is the chance the odds suggest, and it includes the bookmaker's margin. The real chance is unknown.
What is the implied probability of odds of 2.00?
It is 1 ÷ 2.00 × 100 = 50%. The odds suggest the outcome happens about half the time.
Why do the percentages add up to more than 100 percent?
Because the bookmaker adds a margin to every outcome. The extra above 100 percent is the margin, also called the overround.
Do higher odds mean better value?
Not by themselves. Higher odds only mean a lower implied probability. A bet has value only if the real chance is higher than the implied probability.