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

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

Versione interattiva: https://www.calcopenly.com/it/statistics/odds-converter
Argomento: Calcolatori di statistica e probabilità

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%.

## Dati

- **I have** (opzioni: Fractional, Decimal, American, Probabilità)
- **Fractional odds, first number**: 5/2 means win 5 for every 2 staked.
- **Fractional odds, second number**
- **Decimal odds**: Total return per 1 staked, stake included.
- **American odds**: +250: win 250 on a 100 stake. −150: stake 150 to win 100.
- **Probabilità**

## Risultati

- Implied probability — risultato principale
- Decimal odds
- Fractional odds
- American odds
- Profit per 1 staked

## Formula

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

## Esempi svolti

### 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**
- Fonte di verifica: 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%**
- Fonte di verifica: 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%**
- Fonte di verifica: d = 1 + 100/110 = 21/11; p = 11/21 = 52.381% (the standard −110 break-even rate)

### Probability 25%

- I have: Probabilità
- Probabilità: 25%
- **Decimal odds: 4**
- **Fractional odds: 3/1**
- **American odds: +300**
- Fonte di verifica: d = 1/0.25 = 4; 3/1; +300

### Edge case: evens

- I have: Decimal
- Decimal odds: 2
- **Fractional odds: 1/1**
- **American odds: +100**
- **Implied probability: 50%**
- Fonte di verifica: Even money: decimal 2.0 = 1/1 = +100 = 50%

## Domande

### 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%.

### Quanto è preciso «Odds converter (fractional, decimal, American, probability)»?

La precisione dipende dai dati inseriti e dalle ipotesi del metodo. Il calcolo decimale usa 50 cifre significative, ma stime, metodi numerici e dati di origine possono essere meno precisi; l’arrotondamento visualizzato non elimina questi limiti. Esempi svolti verificati con fonti indipendenti: 5. Per esempio, «5/2 (defaults)» viene verificato con d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables).

### Da dove proviene il metodo?

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

## Fonti

- [Grinstead & Snell, Introduction to Probability (AMS), §1.2 — odds and probability](https://math.dartmouth.edu/~prob/prob/prob.pdf)
- [UK Gambling Commission — how odds work (fractional and decimal)](https://www.gamblingcommission.gov.uk/public-and-players/guide/page/how-odds-work)

_Solo per pianificare. Finanziatori, autorità fiscali e mercati applicano propri arrotondamenti, costi e regole; conferma le cifre con loro prima di assumere impegni._