# What does my parlay pay?

Computes the combined odds, payout and profit of a parlay (accumulator) of 2 to 12 legs in American, decimal or fractional odds, with pushed and lost legs.

- Page: https://www.acalculator.org/game/parlay-calculator
- JSON spec: https://www.acalculator.org/game/parlay-calculator.json
- Version: 760c0d546820

## Default answer

Example with the default inputs (Odds format American, Legs [Odds -110, Result Open or won; Odds -110, Result Open or won; Odds +150, Result Open or won], Stake $10.00): A $10.00 parlay at 9.1116 decimal odds pays $91.12 (live or won).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| format | Odds format | The format of every leg’s odds: American, decimal, or fractional. |
| legs | Legs | One row per leg of the parlay: its odds and its result so far. |
| stake | Stake | The amount bet on the parlay. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| payout | Total payout | What the parlay returns: stake × the product of the decimal odds of the legs that count, or 0 if a leg lost. |
| profit | Profit | The payout minus the stake. |
| decimal | Parlay decimal odds | The odds of the ticket: the product of the decimal odds of every leg not pushed (open, won or lost). |
| american | Parlay American odds | The parlay odds in American format, rounded to 2 decimals. |
| fractional | Parlay fractional odds | The exact parlay profit per 1 staked, as a fraction in lowest terms. |
| probability | Implied probability | The chance the parlay odds imply: 100 ÷ the parlay decimal odds (the product of the counted legs’ implied probabilities). |
| counted | Legs that count | The legs not pushed: open, won or lost. |
| status | Status | lost, because a leg lost; refunded, because every leg pushed; otherwise live or won. |

## Method

Parlay decimal odds D = d₁ × d₂ × … over the legs that count (pushed legs drop out); payout = stake × D, or 0 if any leg lost; profit = payout − stake.

## Assumptions

- Legs are independent bets priced separately; the parlay odds are the product of the leg odds. Some bookmakers pay reduced odds on parlays or on same-game parlays.
- A pushed (tied or void) leg drops out, so the parlay pays on the other legs. If every leg pushes, the stake is returned.
- Results are mathematics, not betting advice.

## Worked examples

1. format = american, legs = {"odds":"-110","result":"open"} or {"odds":"-110","result":"open"}, stake = $100.00 gives decimal = 3.644628, american = +264.46, fractional = 320/121, payout = $364.46, probability = 27.437642%. Source: hand calculation in content.mdx: (21/11)² = 441/121; 100 × 441/121 = 364.46.
2. format = american, legs = {"odds":"-110","result":"open"} or {"odds":"-110","result":"open"}, stake = $10.00 gives decimal = 9.11157, american = +811.16, fractional = 1963/242, payout = $91.12. Source: hand calculation in content.mdx: 441/121 × 5/2 = 2205/242; 10 × 2205/242 = 91.12.
3. format = decimal, legs = {"odds":"2","result":"open"} or {"odds":"1.5","result":"push"}, stake = $20.00 gives decimal = 6, american = +500, fractional = 5/1, payout = $120.00, profit = $100.00, counted = 2. Source: hand calculation in content.mdx: the pushed leg drops out; 2 × 3 = 6; 20 × 6 = 120.
4. format = fractional, legs = {"odds":"1/1","result":"open"} or {"odds":"2/1","result":"lose"}, stake = $25.00 gives payout = $0.00, profit = -$25.00, decimal = 6, american = +500, counted = 2, status = lost, because a leg lost. Source: hand calculation in content.mdx: a lost leg loses the whole parlay; the ticket odds stay 2 × 3 = 6.

## FAQ

### How are parlay odds calculated?

Turn each leg’s odds into decimal odds and multiply them. Two legs at −110 are 21/11 × 21/11 = 441/121 = 3.6446 in decimal odds, which is +264.46 in American odds. A 100 stake pays 364.46.

### What happens when a parlay leg pushes?

The pushed leg drops out and the parlay pays on the other legs. A three-leg parlay at decimal 2, 1.5 and 3 with the 1.5 leg pushed pays at 2 × 3 = 6. If every leg pushes, the stake is returned.

### What happens when one leg loses?

The whole parlay loses and pays nothing, however many other legs win.

### What is the implied probability of a parlay?

It is the product of the legs’ implied probabilities, which equals 1 ÷ the parlay decimal odds. Two −110 legs imply 52.38% each and 27.44% together. Each leg’s margin is multiplied too, so a parlay carries more margin than a single bet.

### Why does my bookmaker pay less than this calculator shows?

This calculator multiplies the odds of independent legs. Many bookmakers price same-game parlays lower because the legs are related, and some cap payouts. Check the odds the bookmaker offers for the whole parlay.

## Sources

- Wikipedia, Parlay (gambling): https://en.wikipedia.org/wiki/Parlay_(gambling)
- Wikipedia, Fixed-odds betting (fractional, decimal and moneyline odds): https://en.wikipedia.org/wiki/Fixed-odds_betting
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/