Arbitrage calculator

When two books disagree enough

Add up one divided by each price and you hold the whole market in a single number. Inside one bookmaker that number always clears 100% — the margin is what keeps it there. But the best price on one side and the best price on the other often sit at different books, and combining them can drop the sum below 100%. That is the entire condition: the implied probabilities have to add up to less than 1. Split the total stake in proportion to those implied probabilities and every outcome returns the same amount, so what you get back stops depending on the result. Two prices of 2.10 sum to 95.24%, and 500 on each side of a 1,000 stake returns 1,050 whichever way the match goes.

In practice this closes far less often than the arithmetic suggests, and the reasons matter more than the formula. Prices move: the gap you spotted is usually the slower book catching up, and it can vanish in the seconds between placing the first leg and the second, leaving you holding an ordinary unhedged bet at a price you chose for hedging rather than for value. Stake limits bite hardest exactly where the gap is widest, so a 5% margin on paper is often a 5% margin on forty units rather than on a thousand. And bookmakers restrict accounts that do this systematically — lower limits first, refused bets and closures later. Add the capital parked across several books and the currency spread between them, and arbitrage reads less like a machine and more like a slow, operationally demanding way to shave a thin margin.