The Odds Calculator converts odds for and against into win and lose probabilities, reduces ratios by their greatest common divisor, and translates among fractional, decimal and American formats. Enter a ratio such as 4:48 or a probability percentage; the calculator returns the full set of equivalent figures.
Odds and probability describe the same uncertainty on different scales. Mixing them without converting is a common source of pricing mistakes in games and markets.
Convert odds to probability
Odds for A to B mean A parts win against B parts lose out of A plus B equal parts. Win probability equals A divided by A plus B; lose probability equals B divided by A plus B. Odds against swap the written ratio to B to A without changing those probabilities.
Enter either direction and the calculator fills the rest of the panel.
P(win) = A / (A + B)
P(lose) = B / (A + B)Odds against are the swap: B:A. Enter either direction; the calculator fills the other and both probabilities.
Apply the odds probability formula
For odds for 4 to 48, win probability equals 4 divided by 52, about 0.076923 or 7.6923 percent. Lose probability equals 48 divided by 52, about 92.3077 percent. Reducing 4 to 48 by their greatest common divisor of 4 yields 1 to 12 for display, with odds against 12 to 1. Same facts, smaller integers on the page.
P(win) = 4 / (4 + 48) = 4/52 ≈ 0.076923 (7.6923%). P(lose) = 48/52 ≈ 0.923077 (92.3077%).
Reduce 4:48 by GCD 4 to 1:12 for display. Odds against become 12:1. Same facts, smaller integers.
Convert 4 to 48 odds into a percentage
Total parts equal 52. Win probability is 4 divided by 52 equals 0.076923, shown as 7.6923 percent. Lose probability is 92.3077 percent. Reduced odds for equal 1 to 12 and odds against equal 12 to 1.
That percentage is what a fair price would assign as a win chance before any house margin appears in the quote. 2. Win probability = 4 ÷ 52 = 0.076923 → 7.6923%. 3. Lose probability = 48 ÷ 52 = 0.923077 → 92.3077%. 4. Reduced odds for = 1:12; against = 12:1.
That percentage is what a fair game would charge as a win probability. Bookmakers and casinos often price from payout odds that imply a different percentage; the house-edge section covers that gap.
Read fractional, decimal and American odds
Fractional odds quote profit relative to stake; decimal odds quote total return including stake; American odds quote profit on a 100 stake for underdogs or stake needed to win 100 for favourites.
At win probability 0.076923, fractional odds are 12 to 1, decimal odds are 13.00 and American odds are plus 1200. |---|---|---| | Fractional (UK) | (1 − p)/p : 1, reduced | 12:1 | | Decimal (European) | 1 / p | 13.00 | | American (underdog, p < 0.5) | +100(1 − p)/p | +1200 | | American (favourite, p > 0.5) | −100p/(1 − p) | (not this example) |
Fractional 12:1 means a winning 1-unit stake returns 12 units profit plus stake. Decimal 13.00 returns 13 units total per 1 staked (profit 12). American +1200 means a 100-unit stake wins 1200 profit on an underdog.
Compare implied odds against true odds
Payout odds imply a win probability; the true process may differ. A roulette single-number payout of 35 to 1 implies 1 in 36, about 2.778 percent, while a 38-pocket wheel has true probability 1 in 38, about 2.632 percent. The payout prices the bet as if there were 36 outcomes; the wheel has 38.
- Payout odds 35:1 → implied P(win) = 1/(35+1) = 1/36 ≈ 2.778%.
- European/American wheels with 38 pockets → true P(win) = 1/38 ≈ 2.632%.
The payout prices the bet as if there were 36 equally likely outcomes; the wheel has 38. That gap is the house's edge, not variance.
Calculate the house edge
House edge for the roulette example equals 38 minus 36, divided by 38, which is 5.26 percent. On every unit wagered, the long-run expected loss is about 0.0526 units.
Negative expectation compounds: more independent plays concentrate the average nearer that loss rather than cancelling it into a win over a long series. house edge = (true outcomes − fair payout denominator) / true outcomes ```
Other games publish different edges. A fair coin with even-money payouts has zero edge. A wager that pays 1 to 1 on an event that truly occurs 40 percent of the time has a large negative expectation for the player. Always compare implied probability from the payout with the best available true probability.
For the roulette case: (38 − 36) / 38 = 5.26%. On every unit wagered, the long-run expected loss is about 0.0526 units.
Negative expectation compounds. Doubling the number of independent plays does not "even out" into a win; it concentrates the average result nearer the negative expectation. Short-run luck is real; it does not cancel a built-in edge over a long enough series. That is an honest reading of the math, and it is why comparing implied odds to true odds belongs on this page.
Convert probability back into odds
Given probability 0.2, odds for equal 1 to 4, odds against equal 4 to 1, decimal odds equal 5.00 and American odds equal plus 400. Enter a percentage or decimal probability in the reverse field and the calculator emits every format in the conversion table. Reducing the ratio by GCD keeps the display readable.
- Odds for = 0.2 : 0.8 → multiply by 5 → 1:4.
- Odds against = 4:1.
- Decimal = 1 / 0.2 = 5.00.
- American = +100 × 0.8 / 0.2 = +400.
Enter a percentage or decimal probability in the reverse field; the calculator emits every format in the table above.
Odds in markets versus odds in classrooms
Classroom problems usually treat odds as pure ratios with no vig. Sportsbooks and casinos embed margin in the price, so the implied probabilities for all outcomes often sum to more than 100 percent. That overround is another view of the same edge idea illustrated with roulette.
When converting a bookmaker price for analysis, start from the posted format, translate to implied probability, then compare with an independent estimate of true probability if one exists. The Probability Calculator handles unions and Bayes when the question moves beyond a single price conversion.
Fair odds versus posted prices
Fair odds are the ratio implied by a true probability with no margin. Posted prices embed margin, so converting a posted price to probability and treating that probability as truth mixes the edge into the estimate. When analysing a game, keep three numbers separate: true probability from the process, implied probability from the payout, and the edge as their gap.
Parlay and multi-bet prices compound margins. Even if each leg looks only slightly worse than fair, the combined price can be far from fair. Convert each leg, multiply the fair joint probability under independence if that assumption holds, then compare with the parlay's implied probability to see how fast the edge stacks.
Frequently asked questions
How do I convert odds to probability?
P(win) = A / (A + B) for odds for A:B. For 4:48 that is 4/52 ≈ 7.6923%.
What is the difference between odds for and odds against?
Odds for A:B state win parts to lose parts. Odds against swap them to B:A. Probabilities are unchanged; only the written ratio flips.
What are decimal odds?
Decimal odds equal 1 / P(win). They quote total return per 1 unit staked, including stake.
What are American odds?
Positive American odds (underdogs) show profit on a 100 stake. Negative American odds (favourites) show how much you must stake to win 100 profit.
What is house edge?
House edge is the long-run percentage of each wager the game expects to keep, arising when payout odds imply a higher win chance than the true process offers. It is a long-run average, not a promise about any single wager.
Does a 5.26% house edge mean I lose every bet?
No. Individual bets still win. Over many independent plays the average result trends toward a loss of about 5.26% of total amount wagered.
Are odds the same as probability?
No. Odds are a ratio of win parts to lose parts; probability is win parts over total parts. The calculator converts either way.
Can I enter percentages?
Yes. A probability of 25% converts to odds for 1:3, decimal 4.00 and American +300.
Summary
The Odds Calculator converts between odds and probability, reduces ratios, and translates fractional, decimal and American formats. Odds for 4:48 equal a 7.6923% win chance and reduce to 1:12.
When payout odds disagree with true outcomes, as in 35:1 roulette payouts on a 38-pocket wheel, the gap is a 5.26% house edge with a negative expectation that compounds over repeated play.
Use the Probability Calculator when events need unions, conditionals or Bayes rather than format conversion.