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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.

When to use

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.

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.

Inputs

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

Outputs

Output	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.

Example

Odds 2.20, 50 % chance, stake 100: {"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: {"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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/bet-expected-value (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/bet-expected-value · Markdown: https://tttkmbb.com/gaming/bet-expected-value.md · JSON definition: https://tttkmbb.com/gaming/bet-expected-value.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="bet-expected-value"
OpenAPI operationId: calculate_bet_expected_value
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Expected value (Wikipedia) (reference)
Odds – moneyline, decimal and fractional odds and implied probability (Wikipedia) (reference)

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 calculators

Expected Value Calculator — Expected value and variance of a general list of outcomes and probabilities.
Kelly Criterion Calculator — Optimal stake size for the same odds and probability.
Odds Converter — Convert American or fractional prices to decimal odds.