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Odds converter (fractional, decimal, American, probability)

Convert odds between fractional, decimal and American (moneyline) formats and get the implied probability, worked in exact fractions.

업데이트 검증한 예제: 5

5/2 means win 5 for every 2 staked.
시도하기
Implied probability
%
Implied probability: 28.57 %
최대 소수 자릿수: 2; 가장 가까운 값, 중간값은 0에서 먼 쪽으로
Decimal odds
3.5
Fractional odds
5/2
American odds
+250
Profit per 1 staked
2.5

A 1-unit stake at these odds returns 3.5 in total (2.5 profit) if it wins. The odds imply a 28.57% chance; a bet only has positive expected value if the true chance is higher than that, and bookmakers' prices include a margin, so implied chances across all outcomes add up to more than 100%.

Implied chance

28.57%implied
Win28.57%Lose71.43%
계산 방법 S

  1. Decimal odds (total return per 1 staked)

    d=1+52=3.5d = 1 + \frac{5}{2} = 3.5

    Worked as exact fractions, so no rounding creeps in between formats.

  2. Fractional odds (profit : stake)

    d−1=2.5=5/2d - 1 = 2.5 = 5/2

  3. American odds

    d≥2: +100(d−1)=+250d \ge 2:\ +100(d - 1) = +250

  4. Implied probability

    p=1d=28.571429%p = \frac{1}{d} = 28.571429\%

Odds converter (fractional, decimal, American, probability) 소개

Decimal odds d are the total return per 1 staked, stake included. Fractional odds a/b give the profit per stake, so d = 1 + a/b. American odds are +100(d − 1) when d is 2 or more and −100/(d − 1) when d is below 2, and the implied probability is 1/d. Every conversion runs through exact fractions, so 10/11 stays 10/11 instead of becoming 0.909…

The default, 5/2, is decimal 3.5 and American +250: a 1-unit stake returns 3.5 if it wins, 2.5 of it profit, and the price implies a 28.57% chance. A −110 line, common on US point spreads, implies 52.38%, the win rate needed to break even.

Implied probability describes the price, not the true chance. Bookmakers build a margin into their prices, so the implied probabilities of all outcomes in a market add up to more than 100%.

계산 예제

5/2 (defaults)

I have
Fractional
Fractional odds, first number
5
Fractional odds, second number
2
Decimal odds
3.5
American odds
+250
Implied probability
28.57%
Profit per 1 staked
2.5

검증 출처: d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables)

Decimal 1.5

I have
Decimal
Decimal odds
1.5
Fractional odds
1/2
American odds
−200
Implied probability
66.67%

검증 출처: d − 1 = 1/2; American −100/0.5 = −200; p = 1/1.5 = 2/3

American −110

I have
American
American odds
-110
Decimal odds
1.9091
Fractional odds
10/11
Implied probability
52.38%

검증 출처: d = 1 + 100/110 = 21/11; p = 11/21 = 52.381% (the standard −110 break-even rate)

Probability 25%

I have
확률
확률
25%
Decimal odds
4
Fractional odds
3/1
American odds
+300

검증 출처: d = 1/0.25 = 4; 3/1; +300

자주 묻는 질문

How do you convert fractional odds to decimal odds?

Divide the first number by the second and add 1: d = a/b + 1. So 5/2 becomes 3.5, 1/2 becomes 1.5 and evens (1/1) becomes 2.0. The 1 is the returned stake: fractional odds quote profit only, while decimal odds quote the total return, so a winning 10-unit bet at 5/2 or 3.5 pays back 35 in both cases.

How do American (moneyline) odds work?

A plus number is the profit on a 100 stake and a minus number is the stake needed to win 100. At +250, 100 staked wins 250 profit (decimal 3.5); at −150, 150 staked wins 100 (decimal 1.667). +100 and −100 both mean evens, and no American odds exist between −100 and +100.

How do you convert odds to implied probability?

Divide 1 by the decimal odds: p = 1/d. Decimal 3.5 implies 1/3.5 = 28.57%. For fractional odds a/b the shortcut is b/(a + b), so 5/2 gives 2/7. For American −110 it is 110/(110 + 100) = 52.38%, and for +250 it is 100/(250 + 100) = 28.57%.

What is the overround or bookmaker's margin?

The overround is how far the implied probabilities of every outcome in a market add up past 100%. With both sides of a bet priced at −110, the total is 52.38% + 52.38% = 104.76%, an overround of 4.76% and a bookmaker margin (vig) of 1 − 1/1.0476 = 4.55% of stakes. Dividing each implied probability by the total, 52.38/104.76, removes the margin and gives 50%.

What do odds-on and odds against mean?

Odds-on means the implied probability is above 50%: fractional odds below 1/1, decimal odds below 2.0 and negative American odds. At 1/2 odds-on (1.5, or −200) you stake 2 to win 1, an implied 66.67%. Odds against is the reverse: 5/2 (3.5, or +250) pays more than the stake and implies less than 50%.

“Odds converter (fractional, decimal, American, probability)”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 5. 예를 들어 “5/2 (defaults)”은 d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables)와 대조해 확인합니다.

이 계산 방법의 출처는 무엇인가요?

Grinstead & Snell, Introduction to Probability (AMS), §1.2 — odds and probability; UK Gambling Commission — how odds work (fractional and decimal).

이 계산기 소개

d=1+ab,American={+100(d−1)d≥2−100d−1d<2,p=1dd = 1 + \frac{a}{b},\qquad \text{American} = \begin{cases} +100(d-1) & d \ge 2 \\ -\frac{100}{d-1} & d < 2 \end{cases},\qquad p = \frac1d

출처

  1. Grinstead & Snell, Introduction to Probability (AMS), §1.2 — odds and probability
  2. UK Gambling Commission — how odds work (fractional and decimal)

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