Two modes: Arbitrage splits a stake across two opposing prices for guaranteed profit when the sum of implied probabilities is below 100%. Hedge sizes a counter-bet against an existing position to lock in a fixed outcome regardless of result.
An arbitrage opportunity exists when two opposing markets at two different books, in aggregate, imply less than 100% probability. In that case, a properly-sized split across both sides locks in a profit regardless of outcome. The formula for split sizing: each side gets stake = total × (other side's decimal odds) ÷ (sum of both sides' decimal odds).
Arbs are real but tactical: bookmakers limit, void, or close accounts of bettors who exploit them. Many sharp bettors avoid arbing the same retail book they're trying to keep open for +EV plays. Offshore-to-retail arbs and exchange-to-book arbs are common arbitrage channels.
Hedging is the use case when you already have a position and want to either guarantee a profit (if your original bet is in profit) or limit a potential loss (if it's out of the money). The hedge stake equals: (original stake × original decimal odds) ÷ hedge decimal odds. That sizing locks in the same dollar outcome whether your original bet wins or loses.
The most common hedge scenario: a futures ticket that's now near the finish line. If you hold a +800 NBA Finals MVP ticket and your guy is in the Finals, hedging by betting against him at -200 locks in a guaranteed profit minus the combined vig.