# Bet Expected Value Calculator

> Computes the expected value of a bet from its decimal odds, your estimated win probability and the stake, together with the implied probability, the edge in percentage points and the fair (break-even) decimal odds.

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

## Purpose

Computes the expected value of a bet from its decimal odds, your estimated win probability and the stake, together with the implied probability, the edge in percentage points and the fair (break-even) decimal odds.

**Use when:** You have an estimate of the true win probability and want to know whether a price offers positive expected value, by how much, and what odds would be fair.

**Do not use when:** You need the stake size that maximises bankroll growth (use kelly-criterion), a general probability-weighted mean of several outcomes (use expected-value), or only a format conversion (use odds-converter). Mathematics only; not gambling advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `decimal_odds` | number |  | required | Decimal (European) odds including the stake, e.g. 2.20; convert other formats with odds-converter. (> 1, max 1000000) |
| `win_probability_percent` | number | % | required | Your own estimate of the probability that the bet wins, in percent. (> 0, max 100) |
| `stake` | number |  | optional, default 100 | Amount staked (any currency). (> 0, max 1000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `expected_value` | number |  | Average profit per bet over many repetitions: p·(odds − 1)·stake − (1 − p)·stake. |
| `expected_value_per_unit` | number |  | expected_value / stake = p·odds − 1. |
| `expected_return_percent` | number | % | expected_value_per_unit × 100. |
| `implied_probability_percent` | number | % | 100 / decimal_odds: the win probability at which the bet breaks even. |
| `edge_percent` | number | percentage points | win_probability_percent − implied_probability_percent. |
| `fair_decimal_odds` | number |  | 100 / win_probability_percent: the price at which the expected value is zero. |
| `is_positive_ev` | boolean |  | true when expected_value > 0. |

## Formula

`p = win_probability_percent / 100; expected_value = p·(decimal_odds − 1)·stake − (1 − p)·stake; implied_probability_percent = 100 / decimal_odds; edge_percent = win_probability_percent − implied_probability_percent; fair_decimal_odds = 100 / win_probability_percent`

The expected value is the probability-weighted average of the profit if the bet wins and the loss of the stake if it loses; it is only as good as the probability estimate you supply. Probability mathematics only; not gambling advice.

## Data Sources

- Expected value (Wikipedia) — https://en.wikipedia.org/wiki/Expected_value (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/bet-expected-value?decimal_odds=…&win_probability_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/bet-expected-value` 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/bet-expected-value · OpenAPI operationId `calculate_bet_expected_value` 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": "bet-expected-value", "inputs": {…}}`

## Example

- Odds 2.20, 50 % chance, stake 100: inputs `{"decimal_odds":2.2,"win_probability_percent":50,"stake":100}` → `{"expected_value":10,"expected_value_per_unit":0.1,"implied_probability_percent":45.45,"edge_percent":4.55,"fair_decimal_odds":2,"is_positive_ev":true}`
- Odds 1.80, 50 % chance, stake 50: inputs `{"decimal_odds":1.8,"win_probability_percent":50,"stake":50}` → `{"expected_value":-5,"expected_return_percent":-10,"implied_probability_percent":55.56,"edge_percent":-5.56,"fair_decimal_odds":2,"is_positive_ev":false}`

```
GET https://tttkmbb.com/api/v1/calculate/bet-expected-value?decimal_odds=2.2&win_probability_percent=50&stake=100
```

## Limitations

You need the stake size that maximises bankroll growth (use kelly-criterion), a general probability-weighted mean of several outcomes (use expected-value), or only a format conversion (use odds-converter). Mathematics only; not gambling advice. The expected value is the probability-weighted average of the profit if the bet wins and the loss of the stake if it loses; it is only as good as the probability estimate you supply. Probability mathematics only; not gambling advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Is the edge a percentage or percentage points?**

Percentage points: a 50 % estimate against a 45.45 % implied probability is an edge of 4.55 points. The expected return on stake (10 % here) is the relative figure.

**Where does the win probability come from?**

It must be your own estimate (model, form analysis, removing the margin from market odds); the calculator cannot know the true probability, and a wrong estimate makes the EV wrong.

## Related

- [Expected Value Calculator](https://tttkmbb.com/statistics/expected-value.md) — Expected value and variance of a general list of outcomes and probabilities.
- [Kelly Criterion Calculator](https://tttkmbb.com/gaming/kelly-criterion.md) — Optimal stake size for the same odds and probability.
- [Odds Converter](https://tttkmbb.com/gaming/odds-converter.md) — Convert American or fractional prices to decimal odds.