# Odds Converter

> Converts betting odds between American (moneyline), decimal (European) and fractional (UK) formats, auto-detecting the input format, and reports the implied probability, profit and total return for a stake.

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

## Purpose

Converts betting odds between American (moneyline), decimal (European) and fractional (UK) formats, auto-detecting the input format, and reports the implied probability, profit and total return for a stake.

**Use when:** You have odds in one format and need the other two, the implied probability of a price, or the payout of a stake at those odds.

**Do not use when:** You need the combined price of several selections (use parlay-odds), the value of a bet given your own probability estimate (use bet-expected-value), or a bookmaker's margin across a whole market (use arbitrage-bet). Mathematics only; not gambling advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `odds` | string |  | required | Odds in any format: American +150 or -200, decimal 2.50, fractional 3/2 or 3-2, or evens. |
| `format` | enum: auto \| american \| decimal \| fractional |  | optional, default "auto" | Format of the odds input. Auto: a/b or a-b with digits on both sides is fractional, a sign or an integer of 100 or more is American, anything else is decimal. |
| `stake` | number |  | optional, default 100 | Stake used for the profit and return outputs (any currency). (> 0, max 1000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `american` | string |  | Moneyline price with sign, rounded to a whole number: +X wins X per 100 staked, -X needs X staked to win 100. |
| `decimal` | number |  | Total return per unit staked, including the stake. |
| `fractional` | string |  | Profit/stake as a fraction reduced with the GCD, exactly equal to decimal − 1. |
| `implied_probability_percent` | number | % | 100 / decimal: the break-even win probability the price implies (includes the bookmaker margin). |
| `profit_on_stake` | number |  | stake × (decimal − 1). |
| `total_return` | number |  | stake × decimal (profit plus the returned stake). |
| `detected_format` | string |  | Format the input was parsed as (american, decimal or fractional). |

## Formula

`decimal = 1 + american/100 (american > 0) or 1 + 100/|american| (american < 0); decimal = 1 + a/b (fractional a/b); american = +100·(decimal − 1) if decimal ≥ 2, else −100/(decimal − 1); fractional = (decimal − 1) reduced with the GCD; implied_probability_percent = 100/decimal; total_return = stake × decimal`

Odds of ±100 are evens (2.00, 1/1). The fractional output is the exact reduced fraction of decimal − 1; when a decimal price is a rounded traditional fraction (1.91 for 10/11) the nearest fraction with denominator ≤ 20 within ±0.005 is reported in the notes. Probability mathematics only; not gambling advice.

## Data Sources

- Odds – moneyline, decimal and fractional odds and implied probability (Wikipedia) — https://en.wikipedia.org/wiki/Odds (reference, retrieved 2026-09-24)
- Mathematics of bookmaking – overround and implied probability (Wikipedia) — https://en.wikipedia.org/wiki/Mathematics_of_bookmaking (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/odds-converter?odds=…`
- `POST https://tttkmbb.com/api/v1/calculate/odds-converter` 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/odds-converter · OpenAPI operationId `convert_betting_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: `convert_betting_odds` (dedicated) or `run_calculator` with `{"calculator_id": "odds-converter", "inputs": {…}}`

## Example

- +150 American, stake 100: inputs `{"odds":"+150"}` → `{"american":"+150","decimal":2.5,"fractional":"3/2","implied_probability_percent":40,"profit_on_stake":150,"total_return":250}`
- -200 American: inputs `{"odds":"-200","format":"auto","stake":100}` → `{"american":"-200","decimal":1.5,"fractional":"1/2","implied_probability_percent":66.67,"profit_on_stake":50,"total_return":150}`

```
GET https://tttkmbb.com/api/v1/calculate/odds-converter?odds=%2B150
```

## Limitations

You need the combined price of several selections (use parlay-odds), the value of a bet given your own probability estimate (use bet-expected-value), or a bookmaker's margin across a whole market (use arbitrage-bet). Mathematics only; not gambling advice. Odds of ±100 are evens (2.00, 1/1). The fractional output is the exact reduced fraction of decimal − 1; when a decimal price is a rounded traditional fraction (1.91 for 10/11) the nearest fraction with denominator ≤ 20 within ±0.005 is reported in the notes. Probability mathematics only; not gambling advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How is the format detected automatically?**

Digits on both sides of a slash or dash (3/2, 3-2) mean fractional; a leading + or − sign, or a whole number of 100 or more (150), means American; anything else (2.50, 1.91) is decimal. Set format explicitly if an input is ambiguous.

**Why does 1.91 give 91/100 and not 10/11?**

The fractional output is the exact reduced value of decimal − 1. Bookmakers display 10/11 rounded to 1.91; the closest such traditional fraction (denominator ≤ 20, within ±0.005) is listed in the notes when it differs.

**Why do implied probabilities of a market add up to more than 100 %?**

Each price includes the bookmaker margin (overround). Dividing each implied probability by their sum removes it; arbitrage-bet reports the sum for a whole market.

## Related

- [Parlay Odds Calculator](https://tttkmbb.com/gaming/parlay-odds.md) — Combine several decimal prices into one accumulator price.
- [Bet Expected Value Calculator](https://tttkmbb.com/gaming/bet-expected-value.md) — Compare the implied probability with your own estimate to find the expected value.
- [Percentage Calculator](https://tttkmbb.com/math/percentage.md) — General percent arithmetic on stakes and returns.