A Fair Flip from a Crooked Coin

Two traders need to settle who takes the weekend shift with a fair 50/50 draw, but the only randomizer at hand is a bent coin that lands heads with some unknown probability $p$, where $0 < p < 1$. Using nothing but flips of this bent coin, describe a procedure that produces a perfectly fair 50/50 decision — and explain why it works without knowing $p$.