# Parlay Odds Calculator

> Multiplies the decimal odds of 2–15 independent legs into the combined parlay (accumulator) price and reports the total payout, profit and implied probability of all legs winning.

- Calculator id: `parlay-odds` · Category: Games & Betting Math (`gaming`) · Tool name: `calculate_parlay_odds`
- Canonical page: https://tttkmbb.com/gaming/parlay-odds · This document: https://tttkmbb.com/gaming/parlay-odds.md · JSON definition: https://tttkmbb.com/gaming/parlay-odds.json

## Purpose

Multiplies the decimal odds of 2–15 independent legs into the combined parlay (accumulator) price and reports the total payout, profit and implied probability of all legs winning.

**Use when:** You want the combined odds or payout of a multi-leg parlay, accumulator or multi from the decimal price of each leg.

**Do not use when:** The legs are correlated (same-game parlays are priced differently by bookmakers), you need a single price converted between formats (use odds-converter), or you want to know whether the bet has positive expected value (use bet-expected-value). Mathematics only; not gambling advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `decimal_odds` | number_list |  | required | Decimal odds of every leg, each greater than 1, e.g. 1.91, 2.10, 1.50. Convert American or fractional prices first with odds-converter. |
| `stake` | number |  | optional, default 100 | Amount wagered on the whole parlay (any currency). (> 0, max 1000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `combined_decimal_odds` | number |  | Product of all leg odds. |
| `combined_american` | string |  | The combined price as a signed moneyline, rounded to a whole number. |
| `total_payout` | number |  | stake × combined odds (stake included). |
| `profit` | number |  | total_payout − stake. |
| `implied_probability_percent` | number | % | 100 / combined odds = product of the legs' implied probabilities. |
| `legs` | integer |  | How many selections were combined. |

## Formula

`combined_decimal_odds = Π decimal_odds_i; total_payout = stake × combined_decimal_odds; profit = total_payout − stake; implied_probability_percent = 100 / combined_decimal_odds`

Assumes the legs are independent events so that their implied probabilities multiply; every leg must win for the parlay to pay. The bookmaker margin of each leg compounds in the combined price. Probability mathematics only; not gambling advice.

## Data Sources

- Parlay (gambling) (Wikipedia) — https://en.wikipedia.org/wiki/Parlay_(gambling) (reference, retrieved 2026-09-24)
- Odds – moneyline, decimal and fractional odds and implied probability (Wikipedia) — https://en.wikipedia.org/wiki/Odds (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/parlay-odds?decimal_odds=…`
- `POST https://tttkmbb.com/api/v1/calculate/parlay-odds` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/parlay-odds · OpenAPI operationId `calculate_parlay_odds` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "parlay-odds", "inputs": {…}}`

## Example

- Three legs 1.91, 2.10, 1.50 with stake 100: inputs `{"decimal_odds":[1.91,2.1,1.5],"stake":100}` → `{"combined_decimal_odds":6.0165,"combined_american":"+502","total_payout":601.65,"profit":501.65,"implied_probability_percent":16.62,"legs":3}`
- Four even-money legs with stake 10: inputs `{"decimal_odds":[2,2,2,2],"stake":10}` → `{"combined_decimal_odds":16,"combined_american":"+1500","total_payout":160,"profit":150,"implied_probability_percent":6.25,"legs":4}`

```
GET https://tttkmbb.com/api/v1/calculate/parlay-odds?decimal_odds=1.91%2C2.1%2C1.5&stake=100
```

## Limitations

The legs are correlated (same-game parlays are priced differently by bookmakers), you need a single price converted between formats (use odds-converter), or you want to know whether the bet has positive expected value (use bet-expected-value). Mathematics only; not gambling advice. Assumes the legs are independent events so that their implied probabilities multiply; every leg must win for the parlay to pay. The bookmaker margin of each leg compounds in the combined price. Probability mathematics only; not gambling advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Can I enter American or fractional odds?**

No, each leg must be in decimal form. Convert -110 (1.909) or 3/2 (2.50) with odds-converter first, keeping at least three decimals.

**Why is the implied probability so low?**

It is the product of every leg's implied probability, and each leg carries the bookmaker's margin, so the margin compounds with the number of legs.

## Related

- [Odds Converter](https://tttkmbb.com/gaming/odds-converter.md) — Convert each leg to decimal odds before combining.
- [Probability of Two Events Calculator](https://tttkmbb.com/statistics/probability-of-events.md) — Probability that independent events all occur.
- [Bet Expected Value Calculator](https://tttkmbb.com/gaming/bet-expected-value.md) — Expected value of the parlay from your own probability estimate.