Seen from both sides, "Should I hedge my bet?" leads to one event. Hedging and arbitrage both mean betting on more than one side of the same event. A hedge does it after a first bet is already placed, to lock in part of a win or cut a loss. Arbitrage does it at the start, across different books whose prices disagree, so that every outcome returns a little more than the total stake. What they share is the arithmetic of splitting stakes between opposite results.
Is arbitrage betting allowed? Placing bets on both sides of an event is legal almost everywhere, and is hedge betting legal for the same reason. Books still dislike the practice openly, and does arbitrage betting get you banned is the practical question: accounts that only take arbitrage prices get limited or closed. Is arbitrage betting profitable, then? In small sums and only briefly, until those limits arrive and end the run.
How much to hedge a bet depends on the aim. To guarantee the same return on both sides, divide the first ticket's potential return by the decimal odds of the opposite side, and stake that. To only cover the first stake, bet less. Should I hedge my bet is a question about risk: every hedge pays the book's margin a second time, so a hedge bet strategy used on every ticket slowly costs money.
What does a hedge bet mean in practice? A bettor holds a ticket that now looks likely to win, or likely to lose, and places a second bet on the opposite result. How does hedge betting work in numbers? A parlay needing one last leg at long odds can be hedged by backing the other side of that leg, so the bettor collects something whichever way it goes, at the cost of part of the upside first hoped for.
Prices can move in the moments between two bets, and a changed price can turn a planned arbitrage into an ordinary bet with a loss.
Two books can settle the same event differently, for example on retirements or overtime, which can leave one side of an arbitrage unpaid.
The budget is divided in proportion to the inverse of each best price, so every possible outcome returns about the same total.
Yes. Accounts that only take arbitrage prices tend to be limited or closed, which ends most runs while the sums are still small.