Arbitrage Betting: How the Math Works (with Calculator)

Arbitrage (a two-way "arb") is when different books price the two sides of the same market so generously that you can back both and lock in a profit no matter who wins. It's real, it's rare, and it vanishes in seconds, so the math and the timing both have to be right.

The arbitrage condition

Convert each side's best available price to decimal odds, d. An arbitrage exists when the inverse odds sum to less than one: 1/d₁ + 1/d₂ < 1. That sum is exactly the total you'd stake to guarantee a $1 return, so anything under $1 is locked profit. The further below one, the bigger the margin.

Splitting the stakes

To lock the same return whichever side hits, stake each side in proportion to its inverse odds: side i gets (1/dᵢ) divided by the total inverse sum, times your bankroll. Do it right and both outcomes pay back the same amount, so the profit is fixed before the game starts.

The risks nobody advertises

The arithmetic is the easy part. The hard part is that arbs decay in seconds. A single line move mid-execution can leave you stuck on one side at a bad price. Books also limit or ban accounts that consistently arb, and a voided or misgraded leg breaks the lock entirely. Treat the return figure as a best case and model execution risk explicitly.

This is why arbitrage rewards speed above all: the same tick that opens an arb closes it. The calculator below flags the condition and the stake split. Live, seconds are the whole game.