CalConverters

Odds to Probability Calculator

Convert odds A:B (wins to losses) into win and lose probabilities and percentages, reduced to simplest form, with step-by-step working.

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Odds vs. probability: different denominators, same chance

Odds of A : B compare favorable outcomes (A, wins) to unfavorable ones (B, losses). Probability compares favorable outcomes to the total number of outcomes — wins plus losses. That single difference in denominator is the entire distinction:

Pwin=AA+B,Plose=BA+BP_{\text{win}} = \frac{A}{A + B}, \qquad P_{\text{lose}} = \frac{B}{A + B}

% win=Pwin×100\%\,\text{win} = P_{\text{win}} \times 100

Odds of 5:7 mean 5 favorable outcomes for every 7 unfavorable ones — 12 outcomes total, not 5 or 7.

Worked example: odds of 5 : 7

  1. P(win) = 5/(5 + 7) = 5/12 ≈ 0.4167 → 41.67%
  2. P(lose) = 7/(5 + 7) = 7/12 ≈ 0.5833 → 58.33%
  3. 5 and 7 share no common factor greater than 1, so the odds are already in simplest form: 5 : 7.

Worked example: reducing odds (drawing an Ace)

A standard 52-card deck has 4 Aces (wins) and 48 non-Aces (losses) — odds of 4 : 48:

  1. P(win) = 4/52 ≈ 0.0769 → 7.69%
  2. Both 4 and 48 share a greatest common divisor of 4, so the odds reduce: 4 : 48 = 1 : 12.
Tip: Reducing odds works exactly like simplifying a fraction — divide both sides by their GCD. 1:12 and 4:48 describe the identical 7.69% chance; 1:12 is just the smaller, tidier way to write it.

True odds vs. implied (betting) odds

Not every "odds" you see is the true probability. Betting odds are a payout ratio set by the house, and they usually imply a slightly worse chance than reality — the gap is the house edge.

Roulette example: a single-number bet in American roulette pays 35 : 1. Taken at face value, that payout implies a probability of 1/(35 + 1) = 1/36 ≈ 2.78%. But an American roulette wheel has 38 pockets (numbers 1-36, plus 0 and 00), so the true probability of any one number is 1/38 ≈ 2.63%.

That small gap — 2.78% implied vs. 2.63% true — is the house edge. The casino pays out as if there were 36 equally likely outcomes, while there are actually 38. Over many spins, that difference is what keeps the odds in the house's favor.

Tip: Whenever you see a betting line like "35:1" or "3:2", treat it as a payout ratio first, not automatically the real-world probability. Compare the implied probability (from the posted odds) against any independent estimate of the true probability to see how large the built-in edge is.

Common mix-ups

  • Odds 1:499 is not a 1-in-499 chance. It is 1 win for every 499 losses — 500 outcomes total — so the probability is 1/500 (0.2%), not 1/499.
  • "Odds for" and "odds against" are opposites. 5:7 for winning is the same event as 7:5 against winning — check which side A and B represent before reading a result.
  • Posted betting odds are not automatically true odds — see the house-edge example above.

Where this shows up

Converting odds to probability comes up in betting and gambling (reading a sportsbook or casino payout line), games of chance (card odds, dice odds), and everyday risk framing ("a 1-in-4 chance" vs. "odds of 1:3"). For another "part vs. whole" calculation with the same A-over-total shape, see vote percentage; for the general percentage formula this builds on, see percentage.

Frequently asked questions

What is the difference between odds and probability?
They compare different things. Odds of A:B compare wins to losses (A to B) — a ratio between two outcomes. Probability compares wins to the total number of outcomes — A to (A + B). The two describe the same underlying chance, just against different denominators, which is why odds 1:1 (even odds) is a 50% probability, not 100%.
Do odds of 1:499 mean a 1-in-499 chance?
No — this is one of the most common mix-ups. Odds of 1:499 mean 1 favorable outcome for every 499 unfavorable ones, so there are 500 total outcomes, and the probability is 1/500 (0.2%), not 1/499. Always add A and B together to get the total before computing a percentage from odds.
What does it mean to reduce odds, like 4:48 to 1:12?
Reducing odds divides both sides by their greatest common divisor (GCD), the same way you simplify a fraction — 4:48 and 1:12 describe the identical chance, just written with smaller numbers. This calculator only reduces when both A and B are whole numbers; odds like 1.5:2.5 have no whole-number GCD to divide by, so they are left as entered.
Why are a casino's posted odds different from the true odds?
A posted payout like 35:1 on a single roulette number implies a 1-in-36 chance, but American roulette has 38 pockets (1-36 plus 0 and 00), so the true chance of any one number is 1-in-38. That gap between the implied odds and the true odds is the house edge — it is baked into the payout so that, over many spins, the casino keeps a small percentage of every dollar wagered.
What's the difference between "odds for" and "odds against"?
"Odds for" winning and "odds against" winning are mirror images of each other. Odds of 5:7 for winning are the same event as odds of 7:5 against winning — swapping A and B swaps which side is being described. Enter A as the side whose probability you want (wins), and B as the other side (losses).
Can A or B be a decimal, like 1.5:2.5?
Yes — this calculator accepts non-negative decimals as well as whole numbers, since odds sometimes come from decimal source data (like weighted counts). The probability math (A divided by A + B) works the same either way; only the GCD-based reduction step is skipped, since reducing to whole-number lowest terms only makes sense when both sides are already whole numbers.

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