Why is it optimal to size the hedge bet such that you get the same payout for either outcome? Why does that have greater EV than if the bets are skewed in either direction?
EV is the same, you’re just reducing volatility (risk is maybe a better word?) by guaranteeing the outcome either way. A downside is that the hedge does increase the necessary bankroll. That said EV does vary with how long the odds are.
Why is it optimal to size the hedge bet such that you get the same payout for either outcome? Why does that have greater EV than if the bets are skewed in either direction?
EV is the same, you’re just reducing volatility (risk is maybe a better word?) by guaranteeing the outcome either way. A downside is that the hedge does increase the necessary bankroll. That said EV does vary with how long the odds are.
Oh, I see. Yes, this is what I thought—the EV doesn’t change but you can reduce your exposure to particular outcomes.