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Arbitrage calculator for 2-way and 3-way markets

Check whether the best odds across bookmakers or prediction markets form an arbitrage, and split a total stake across 2 or 3 outcomes for an equal return. Free and private.

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Last updated: · Written and reviewed by Ken Lin

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Quick answer

Enter the best available odds for each outcome (2 or 3) and a total stake. If the implied probabilities sum to less than 100% there is an Arbitrage; the calculator shows the profit margin and how to split the stake so every outcome returns the same amount [1].

Calculator

Arbitrage: the best prices sum to less than 100%.

Sum of implied probabilities95.24%
Profit margin5.00%
Return105.00
Profit5.00
OutcomeDecimalStakeReturn
Outcome 12.10050.00105.00
Outcome 22.10050.00105.00

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How it works, with an example

An arbitrage exists when Σ 1/odds < 1 [2]. Splitting the stake in proportion to each outcome's implied probability makes the return identical whichever outcome wins. Example: 2.10 and 2.10 with a total of 100 → implied 47.62% + 47.62% = 95.24%; stake 50 on each; return 105.00; profit 5.00 (a 5.00% margin). Odds-API.io's arbitrage endpoint uses the same margin formula and nets out exchange commission [3]. Real-world caveats: prices move within seconds, stakes can be capped, and accounts can be limited [2].

Formula

arb exists if Σ 1 / oddsᵢ < 1
profit margin = (1 − Σ 1/oddsᵢ) / Σ 1/oddsᵢ
stakeᵢ = total stake × (1/oddsᵢ) / Σ 1/oddsⱼ
return = total stake / Σ 1/oddsⱼ

Feed it live odds

Arbitrage windows are short, so they are found by software scanning many books at once. Odds-API.io Partner link has a dedicated arbitrage endpoint that returns opportunities with the legs, profit margin and suggested stakes, including Polymarket and Kalshi legs [3].

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Frequently asked questions

Is arbitrage risk-free?

Only at the quoted prices. Odds can change before every leg is placed, stakes can be limited, and void or settlement rules differ between platforms, so treat “risk-free” as a calculation, not a guarantee.

Does it handle exchange commission?

Enter net odds: for a back price p with commission c, net odds = 1 + (p − 1) × (1 − c). Odds-API.io reports net odds for exchange legs.

Why only 2 or 3 outcomes?

Most arbitrages are on two-way markets (moneyline, totals, spreads) or three-way football markets. The same formula works for more outcomes.

About this guide

Pred-Data publishes independent, source-linked explainers about prediction markets and the AI tools used around them. Every factual claim on this page links to a primary or reputable secondary source, checked on the date shown above. We do not run a trading venue, take bets, or give personal advice.

Author: Ken Lin · Corrections: if you spot an error, we review it and date-stamp the fix.

Affiliate disclosure

Some links on this site (marked “Partner link”) may be affiliate links: if you sign up through them we may earn a commission at no extra cost to you. Partner links use rel="sponsored nofollow" and never change our assessment. Platform links in our comparison tables are plain, non-affiliate links to official sites.

Sources

  1. Arbitrage Calculator for 2-Way and 3-Way Markets — Odds-API.io tools, accessed 2 Nov 2026
  2. What Is Arbitrage Betting? Definition & Example — Odds-API.io glossary, accessed 2 Nov 2026
  3. Arbitrage Bets guide (formula, response format, limitations) — Odds-API.io docs, accessed 2 Nov 2026