Weighing both sides of "How much to hedge a 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 results on opposite sides.
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 real money.
How to find arbitrage betting opportunities is mostly a matter of speed. Prices differ between books for minutes at a time, often after news, and the gap is usually one or two percent. Arbitrage betting risks are real despite the promise of a sure thing: a price can move before the second bet is placed, a bet can be voided for a palpable error, and settlement rules can differ between books.
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.
Quick answers
How can a bettor tell that an arbitrage exists?
Add up one divided by each best price across all outcomes; when the total falls below one, the prices leave room for a guaranteed return.
What is a hedge bet?
A second bet on the opposite result, placed after a first ticket already stands, to lock in part of a win or reduce a likely loss.
Why compare settlement rules between books?
Two books can settle the same event differently, for example on retirements or overtime, which can leave one side of an arbitrage unpaid.
What is a palpable error in arbitrage betting?
A price the book considers obviously wrong can be voided under its terms, leaving the other half of the arbitrage standing alone.
Does hedging every bet cost money?
Yes. Each hedge pays the book's margin a second time, so a habit of hedging every ticket slowly eats into the overall return.