We show that the existence of a coin-flipping protocol safe against any non-trivial constant bias (e.g., 499 ) implies the existence of one-way functions. This improves upon a recent result of Haitner and Omri [FOCS '11], who proved this implication for protocols with bias 2 2 − 1 − o (1) 207 . Unlike the result of Haitner and Omri, our result also holds for weak coin-flipping protocols.