Dutching / arbitrage calculator
Two outcomes, two prices, one stake. See exactly how much to bet on each so the return is identical whichever wins — and whether that return beats the stake.
Implied probabilities sum to less than 100%: this split returns the same amount whichever outcome wins. Sportsbook prices carry no explicit fee; prediction-market legs would still owe taker fees.
The math
Convert each price to an implied probability p. The stake share for a side is p divided by the sum of both p's. If the sum is below 1, the equal return exceeds the stake and the position is an arbitrage; the profit as a fraction of stake is 1 / sum − 1.
Example: +120 (p = 0.4545) and −105 (p = 0.5122) sum to 0.9667. On $1,000, bet $470 at +120 and $530 at −105; either way the return is $1,034 — a $34 profit (3.4%).
What can go wrong
The second bet must land before the second book moves; displayed prices may not be available at your size; both bets must be on the identical line (a −1.5 at one book and −2 at another is a middle, not an arb); and both books must be available in your state. The live dashboard checks the first three for every card it shows.
Frequently asked questions
How do you split an arbitrage bet?
Stake on each outcome in proportion to its implied probability. With decimal odds A and B and total stake S: bet S·(1/A)/(1/A + 1/B) on A and S·(1/B)/(1/A + 1/B) on B. Each returns S / (1/A + 1/B); if that is more than S, the difference is locked-in profit.
How much profit does arbitrage make?
Cross-book edges are usually 0.5–5% of the stake; our 30-day measurements across 20+ US books average around 1–2% on real, identical-line disagreements. The larger the edge, the shorter the window and the higher the chance one book has already moved.
Does this include fees?
Sportsbooks charge no explicit fee — their cost is already in the odds — so this calculator is exact for book-vs-book. Prediction-market legs owe taker fees on top; the opportunity calculator and the Kalshi/Polymarket fee calculators handle those.
Related: What dutching is · Which books disagree most · Opportunity calculator (with fees) · Vig calculator
Educational tool. Verify every price on the venue before acting; nothing here is financial or betting advice.