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Odds ⇄ Probability Trainer

Convert between decimal odds, fractional odds and probability at speed, the mental plumbing of every betting and options market.

Odds ⇄ Probability Trainer

Decimal odds are just 1 ÷ probability, so 2.0 means 50% and 4.0 means 25%. Fractional odds a/b (a-to-b against) imply a probability of b/(a+b), 3/1 is 25%, 1/1 is 50%. Fluent conversion between the two is core numeracy for trading, market making and prediction markets.

Learn how it works

Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.

Decimal odds 2.0 to probability

A bet has decimal odds of 2.0. What implied probability is that?

Show solution

Probability = 1 ÷ decimal odds:

  • 1 ÷ 2.0 = 0.50 = 50%

Decimal 2.0 is the classic "evens" bet, a coin flip. Your stake doubles if you win.

Decimal odds 4.0 to probability

A bet has decimal odds of 4.0. What implied probability is that?

Show solution

Same one-line rule, probability = 1 ÷ decimal odds:

  • 1 ÷ 4.0 = 0.25 = 25%

Bigger decimal odds mean a longer shot: 4.0 implies it happens only one time in four.

Fractional odds 3/1 to probability

A bet is quoted at fractional odds of 3/1 ("three to one"). What is the implied probability?

Show solution

For fractional a/b, probability = b ÷ (a + b):

  • here a = 3, b = 1
  • = 1 ÷ (3 + 1) = 1 ÷ 4 = 25%

Read it as: 3 losing chances for every 1 winning chance → 1 out of every 4 → 25%.

Probability 80% to decimal odds

You think an event has an 80% chance. What decimal odds does that correspond to?

Show solution

Decimal odds = 1 ÷ probability:

  • 1 ÷ 0.80 = 1.25

A near-certainty pays little: decimal 1.25 means a $1 winning bet returns just $1.25 total. Short odds for a likely event.

Probability 20% to fractional odds

You think an event has a 20% chance. What fractional odds is that?

Show solution

Fractional odds compare losing chances to winning chances = (1 − p) ÷ p:

  • (1 − 0.20) ÷ 0.20 = 0.80 ÷ 0.20 = 4
  • so 4/1 ("four to one")

Sanity check with the earlier rule: b ÷ (a + b) = 1 ÷ (4 + 1) = 1/5 = 20%.

What you'll learn

Fluent, fast conversion between odds and probability, a core numeracy skill for trading, market making and prediction markets.