Place the hedge stake at — on the opposing outcome to guarantee the same payout regardless of which side wins.
The classic case: a long-shot futures bet (Super Bowl, Conference winner, World Series) has reached the late stages and the price on your side has shortened dramatically. You can either let it ride (high variance, high upside) or hedge to lock in profit.
The math: if your $100 ticket on the Chiefs at +800 to win the Super Bowl could pay $900 ($800 profit), and the day before the game the Chiefs are -120 to beat the Eagles, you can lay roughly $750 on the Eagles at +100 to guarantee roughly $150 profit either way. The original bet's expected value is partially preserved while removing all variance.
Don't hedge automatically — sometimes letting the variance ride is the +EV move. But always run the math.