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Market analysis

Odds converter and implied probability

The world's betting cultures write the same price in different formats: decimal, fractional or the signed American style. This converter shows the same odds in the different formats and computes the implied probability behind it, i.e. the chance the price builds in.
Calculators
Analysis, not advice. The calculators' output is a mathematical illustration for the course chapters, not a betting recommendation, stake suggestion or financial advice. Every decision is your own responsibility.

Odds converter

Enter the odds in any format and get the other two, plus the implied probability.

Enter valid odds: a decimal greater than 1, an American with an absolute value of at least 100, or a fraction in a/b form.

Chapter 3: Implied probability

The formulas

implied probability = 1 / decimal odds. Fractional a/b: decimal = 1 + a/b. American: if positive, decimal = 1 + american/100; if negative, decimal = 1 + 100/|american|.

Worked example

Decimal odds of 2.50 are 6/4 in fractional and +150 in American format. The implied probability is 1/2.50 = 40%: the price says the outcome would need to come in four times out of ten to break even. In reverse: American -125 is 1 + 100/125 = 1.80 in decimal, and fractional 7/4 is 1 + 7/4 = 2.75.

Anchor points

A few levels worth knowing by heart: 1.25 = 80% (4 out of 5 needed to break even), 1.50 = 1/2 = -200 = 66.7%, 2.00 = 1/1 = +100 = 50%, 2.50 = 6/4 = +150 = 40%, 3.00 = 33.3%, 5.00 = 20%, 10.00 = 10%. The implied probabilities of a full market always sum above 100%: the excess is the bookmaker margin, typically around 5% on main 1X2 markets.

Common misunderstanding

Decimal odds include the stake: 10,000 staked at 1.85 returns a payout of 18,500, of which the profit is 8,500, and mixing the two up is a classic beginner mistake. Also, the implied probability is a price, not the true chance: it contains the bookmaker's margin, which is why a full market sums above 100%.

01

How do I turn odds into a probability?

For decimal odds, divide 1 by the odds: 2.00 = 50%, 4.00 = 25%. This is also the break-even point: above that hit rate the price is profitable in the long run, below it losing.

02

How do I convert fractional odds to decimal?

Add 1 to the fraction: 5/1 = 6.00, 6/4 = 2.50, 1/2 = 1.50. The fractional format states the net profit relative to the stake and does not include the stake, so its decimal counterpart is always one higher.

03

What do negative American odds mean?

That the outcome is the favourite: the number states how much must be risked to win 100 units. -200 is 1.50 in decimal. Positive American odds state the profit per 100 units staked: +150 is 2.50 in decimal.

04

Why do a market's probabilities sum to more than 100%?

Because the odds contain the bookmaker's margin. If both sides of a two-way market are 1.90, the sum is 105.3%: the excess is the bookmaker's built-in cost.

05

Are there other formats too?

Yes: Hong Kong odds are the decimal minus 1, Malay odds always sit between -1 and +1, and Indonesian odds are the American divided by 100. Each answers the same question with a different reference point; the common language is decimal.