{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"arbitrage-bet"},"result":{"entity_type":"calculator","id":"arbitrage-bet","calculator_id":"arbitrage-bet","canonical_url":"https://tttkmbb.com/gaming/arbitrage-bet","name":"Arbitrage Betting Calculator","title":"Arbitrage Bet Calculator – Arb Percentage, Stake Split and Guaranteed Profit from Best Odds","category":"gaming","category_name":"Games & Betting Math","tool_name":"calculate_arbitrage_bet","featured_mcp_tool":false,"description":"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.","use_when":"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.","inputs":[{"name":"decimal_odds","label":"Best decimal odds per outcome","type":"number_list","required":true,"description":"The best decimal odds available for each outcome of the market (2 outcomes, or 3 for home/draw/away), each greater than 1.","example":[2.1,2.05]},{"name":"total_stake","label":"Total stake","type":"number","required":false,"default":1000,"max":1000000000,"exclusive_min":0,"description":"Total amount to spread across the outcomes (any currency).","example":1000}],"outputs":[{"name":"arbitrage_percentage","label":"Arbitrage percentage","type":"number","unit":"%","decimals":2,"description":"Σ 100/odds_i: the combined implied probability (market overround from the bettor's side)."},{"name":"arbitrage_exists","label":"Arbitrage exists","type":"boolean","decimals":4,"description":"true when the arbitrage percentage is below 100 %."},{"name":"profit_percent","label":"Profit on total stake","type":"number","unit":"%","decimals":2,"description":"(100 / arbitrage_percentage − 1) × 100; negative when no arbitrage exists."},{"name":"stakes","label":"Stake per outcome","type":"number_list","decimals":2,"description":"total_stake × (1/odds_i) / Σ(1/odds), in the order of the input odds."},{"name":"guaranteed_payout","label":"Guaranteed payout","type":"number","decimals":2,"description":"Return whichever outcome wins: total_stake / Σ(1/odds) (the same for every outcome)."},{"name":"guaranteed_profit","label":"Guaranteed profit","type":"number","decimals":2,"description":"guaranteed_payout − total_stake."},{"name":"implied_probabilities_percent","label":"Implied probability per outcome","type":"number_list","unit":"%","decimals":2,"description":"100/odds_i for each outcome."}],"input_schema":{"type":"object","properties":{"decimal_odds":{"description":"The best decimal odds available for each outcome of the market (2 outcomes, or 3 for home/draw/away), each greater than 1.","type":"array","items":{"type":"number"},"minItems":2,"examples":[[2.1,2.05]]},"total_stake":{"description":"Total amount to spread across the outcomes (any currency).","type":"number","maximum":1000000000,"exclusiveMinimum":0,"default":1000,"examples":[1000]}},"additionalProperties":false,"required":["decimal_odds"]},"output_schema":{"type":"object","properties":{"arbitrage_percentage":{"description":"Σ 100/odds_i: the combined implied probability (market overround from the bettor's side). Unit: %.","type":"number","x-unit":"%"},"arbitrage_exists":{"description":"true when the arbitrage percentage is below 100 %.","type":"boolean"},"profit_percent":{"description":"(100 / arbitrage_percentage − 1) × 100; negative when no arbitrage exists. Unit: %.","type":"number","x-unit":"%"},"stakes":{"description":"total_stake × (1/odds_i) / Σ(1/odds), in the order of the input odds.","type":"array","items":{"type":"number"}},"guaranteed_payout":{"description":"Return whichever outcome wins: total_stake / Σ(1/odds) (the same for every outcome).","type":"number"},"guaranteed_profit":{"description":"guaranteed_payout − total_stake.","type":"number"},"implied_probabilities_percent":{"description":"100/odds_i for each outcome. Unit: %.","type":"array","items":{"type":"number"},"x-unit":"%"}}},"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","method":"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.","sources":[{"name":"Arbitrage betting (Wikipedia)","url":"https://en.wikipedia.org/wiki/Arbitrage_betting","type":"reference","retrieved_at":"2026-09-24"},{"name":"Mathematics of bookmaking – overround and implied probability (Wikipedia)","url":"https://en.wikipedia.org/wiki/Mathematics_of_bookmaking","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Two-way 2.10 and 2.05, total 1000","inputs":{"decimal_odds":[2.1,2.05],"total_stake":1000},"expected":{"arbitrage_percentage":96.4,"arbitrage_exists":true,"profit_percent":3.73,"stakes":[493.98,506.02],"guaranteed_payout":1037.35,"guaranteed_profit":37.35},"url":"https://tttkmbb.com/api/v1/calculate/arbitrage-bet?decimal_odds=2.1%2C2.05&total_stake=1000"},{"name":"Two-way 1.91 and 1.91 (no arbitrage)","inputs":{"decimal_odds":[1.91,1.91],"total_stake":1000},"expected":{"arbitrage_percentage":104.71,"arbitrage_exists":false,"profit_percent":-4.5,"stakes":[500,500],"guaranteed_payout":955,"guaranteed_profit":-45},"url":"https://tttkmbb.com/api/v1/calculate/arbitrage-bet?decimal_odds=1.91%2C1.91&total_stake=1000"}],"faq":[{"q":"Why do the stakes not add up to a round number per outcome?","a":"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."},{"q":"Does this include exchange commission?","a":"No. On a betting exchange reduce the net odds first, e.g. net = 1 + (odds − 1) × (1 − commission), then enter the net decimal odds."}],"tags":["arbitrage betting","arb calculator","sure bet","dutching","overround","stake split"],"related":[{"calculator_id":"hedge-bet","reason":"Cover a bet you already hold instead of staking all outcomes fresh."},{"calculator_id":"odds-converter","reason":"Convert each bookmaker's price to decimal odds."},{"calculator_id":"percentage","reason":"Percent arithmetic on the stake split."}],"links":{"html":"https://tttkmbb.com/gaming/arbitrage-bet","markdown":"https://tttkmbb.com/gaming/arbitrage-bet.md","json":"https://tttkmbb.com/gaming/arbitrage-bet.json","api":"https://tttkmbb.com/api/v1/calculate/arbitrage-bet","schema":"https://tttkmbb.com/api/v1/calculators/arbitrage-bet","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:44Z"}