The two-sided quote that loses on every fill

You post $98$ bid / $102$ ask on a contract you believe is worth $100$. Your counterparty, though, knows the true value $V$, which turns out to be equally likely $96$ or $104$. They trade only when it's profitable for them, buying your offer if $V$ is high, selling to your bid if $V$ is low.

What is your expected profit on this trade? How wide would you have had to quote to avoid a guaranteed loss?