Arbitrage Calculator
Arbitrage calculator works out Decimal odds and American / moneyline odds from Odds format, Stake and Odds for each leg or outcome. The default figures on this page give guaranteed return on stake of 3.73494 %; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Sum of implied probabilities = 1/2.1 + 1/2.05 = 0.96399535
- That is below 1, so an arbitrage exists: every unit staked returns 1.0373494.
- Stakes in proportion to 1/d: 493.98, 506.02.
Stake on each outcometable
| outcome | decimal | stake | returnIfItWins |
|---|---|---|---|
| 1 | 2.1 | 493.98 | 1,037.35 |
| 2 | 2.05 | 506.02 | 1,037.35 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the arbitrage calculator calculates
Converts between American, decimal, fractional and implied-probability odds, works out payouts and parlay returns, strips the bookmaker margin to give no-vig fair prices, finds arbitrage stakes across books, sizes a bet by the Kelly criterion and computes hedge stakes and martingale sequences.
How to use this arbitrage calculator
Enter Odds format, Stake, Odds for each leg or outcome and Kelly fraction. Decimal odds updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Decimal odds, American / moneyline odds and Fractional odds.
The method follows Kelly, J.L. Jr (1956), "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 917-926, Thorp, E.O. (2006), "The Kelly Criterion in Blackjack, Sports Betting and the Stock Market", Handbook of Asset and Liability Management, Elsevier, Cortis, D. (2015), "Expected values and variances in bookmaker payouts: a theoretical approach towards setting limits on odds", Journal of Prediction Markets 9(1), 1-14 and Shin, H.S. (1993), "Measuring the incidence of insider trading in a market for state-contingent claims", The Economic Journal 103(420), 1141-1153.
What you can compare
Change one input at a time to see how it affects Decimal odds, American / moneyline odds and Fractional odds. The inputs you can vary are Odds format, Stake, Odds for each leg or outcome and Kelly fraction.
Understanding Decimal odds, American / moneyline odds and Fractional odds
This is an arithmetic tool, not betting advice. Bookmaker prices already carry a margin, so the long-run expected value of a bet at posted odds is negative unless you genuinely have an edge. Gamble only what you can afford to lose.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What is the best platform for arbitrage?
On the figures this page opens with — stake 100 — the guaranteed return on stake is 3.73494%. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
Does arbitrage guarantee profit?
Converts between American, decimal, fractional and implied-probability odds, works out payouts and parlay returns, strips the bookmaker margin to give no-vig fair prices, finds arbitrage stakes across books. On the figures this page opens with — stake 100 — the guaranteed return on stake is 3.73494%. Put your own figures in their place and the working updates beside the result.
How to calculate if there is arbitrage?
Converts between American, decimal, fractional and implied-probability odds, works out payouts and parlay returns, strips the bookmaker margin to give no-vig fair prices, finds arbitrage stakes across books. Open “How this is worked out” beside the result to see each step for your own figures.
Can you make money on arbitrage?
It needs Odds format, Stake, Odds for each leg or outcome and Kelly fraction. Nothing else is required, and the figures stay in your browser.
What information do I need for the arbitrage calculator?
You need Odds format, Stake, Odds for each leg or outcome and Kelly fraction. The page opens with default figures that give guaranteed return on stake of 3.73494 %, so you can see the scale before entering your own.
What does this arbitrage calculator show?
It shows Decimal odds, American / moneyline odds, Fractional odds, Implied probability, Hong Kong odds, Indonesian odds, Malay odds and Profit if the bet wins, with the working and any warnings for your entries.