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Arbitrage Betting Calculator
Sums the implied probabilities of the best decimal odds available on each outcome of a 2- or 3-way market, tests whether an arbitrage exists (sum below 100 %) and splits a total stake so that every outcome returns the same payout.
When to use
You have the best price for each outcome of a market (from different bookmakers or an exchange) and want to know whether the prices overlap, how to split the stake, and the guaranteed return.
Do not use when: You already hold one bet and want to cover it (use hedge-bet), or the market has more than three outcomes. Mathematics only; not gambling advice: stake limits, voided bets and stake rounding can turn a paper arbitrage into a loss.
Formula
arbitrage_percentage = Σ (100 / odds_i); arbitrage_exists = arbitrage_percentage < 100; stake_i = total_stake × (1/odds_i) / Σ(1/odds); guaranteed_payout = total_stake / Σ(1/odds); guaranteed_profit = guaranteed_payout − total_stake; profit_percent = (100 / arbitrage_percentage − 1) × 100
Dutching arithmetic: stakes proportional to each outcome's implied probability make every outcome pay the same amount. Exchange commission and stake rounding are not modelled. Probability mathematics only; not gambling advice.
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
decimal_odds | number_list | yes | The best decimal odds available for each outcome of the market (2 outcomes, or 3 for home/draw/away), each greater than 1. | |
total_stake | number | default 1000 | Total amount to spread across the outcomes (any currency). Range: > 0, ≤ 1000000000 |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
arbitrage_percentage | number | % | Σ 100/odds_i: the combined implied probability (market overround from the bettor's side). |
arbitrage_exists | boolean | true when the arbitrage percentage is below 100 %. | |
profit_percent | number | % | (100 / arbitrage_percentage − 1) × 100; negative when no arbitrage exists. |
stakes | number_list | total_stake × (1/odds_i) / Σ(1/odds), in the order of the input odds. | |
guaranteed_payout | number | Return whichever outcome wins: total_stake / Σ(1/odds) (the same for every outcome). | |
guaranteed_profit | number | guaranteed_payout − total_stake. | |
implied_probabilities_percent | number_list | % | 100/odds_i for each outcome. |
Example
Two-way 2.10 and 2.05, total 1000: {"decimal_odds":[2.1,2.05],"total_stake":1000} → {"arbitrage_percentage":96.4,"arbitrage_exists":true,"profit_percent":3.73,"stakes":[493.98,506.02],"guaranteed_payout":1037.35,"guaranteed_profit":37.35}
Two-way 1.91 and 1.91 (no arbitrage): {"decimal_odds":[1.91,1.91],"total_stake":1000} → {"arbitrage_percentage":104.71,"arbitrage_exists":false,"profit_percent":-4.5,"stakes":[500,500],"guaranteed_payout":955,"guaranteed_profit":-45}
GET https://tttkmbb.com/api/v1/calculate/arbitrage-bet?decimal_odds=2.1%2C2.05&total_stake=1000
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/arbitrage-bet(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/arbitrage-bet · Markdown: https://tttkmbb.com/gaming/arbitrage-bet.md · JSON definition: https://tttkmbb.com/gaming/arbitrage-bet.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="arbitrage-bet" - OpenAPI operationId:
calculate_arbitrage_bet - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
FAQ
Why do the stakes not add up to a round number per outcome?
They are the exact proportional split; rounding each stake to whole units changes the payouts slightly, so recompute the payout of each outcome (stake × odds) after rounding.
Does this include exchange commission?
No. On a betting exchange reduce the net odds first, e.g. net = 1 + (odds − 1) × (1 − commission), then enter the net decimal odds.
Related calculators
- Hedge Bet Calculator — Cover a bet you already hold instead of staking all outcomes fresh.
- Odds Converter — Convert each bookmaker's price to decimal odds.
- Percentage Calculator — Percent arithmetic on the stake split.