Arbitrage in one line
An arbitrage exists when the best available price for every outcome, taken across different bookmakers, has implied probabilities that add up to less than 100%. Split a stake across those prices in the right proportions and every outcome pays back more than was staked.
A worked example
Bookmaker A offers 2.10 on Team X, bookmaker B offers 2.15 on Team Y, a straight two-way market. Implied probabilities: 1 ÷ 2.10 = 47.6%, 1 ÷ 2.15 = 46.5%, adding up to 94.1%, under 100%. Staking roughly 50.6 on X and 49.4 on Y (100 total) returns about 106.2 whichever side wins: a locked-in 6.2% profit.
Why it's harder than it looks
The prices have to be live at both bookmakers at the same moment you place both bets; odds move, and a price can vanish between the first bet and the second. It also needs a funded account at every bookmaker involved, in the same currency ideally, and the stake has to be split precisely for the numbers to work.
Bookmakers actively look for arbing patterns, since an account that always bets both sides of a market is a clear tell, and they tend to limit or close those accounts faster than accounts that just win.
Arbitrage vs. +EV betting
Arbitrage is close to risk-free on a single event, but the margins are usually small and fragile, and the account-limiting problem is worse than for +EV betting. +EV betting takes on real variance on every individual bet, but a real edge doesn't depend on catching a rare price gap, and it's the approach Sharp Bets is built around: find prices better than the fair odds, size the stake to the edge, and let the sample size do the work over hundreds of bets rather than one.