I was reading Richard Cleve's 1984 paper on coin flipping protocols, and he says that in the case where parties may abort prematurely and the honest party is forced to output a bit, then the honest party can be forced to be biased by at least 1/r where r is the number of rounds.
Recently Moran, Naor, Segev showed that this bound is asympotically tight.
Although I roughly understand Cleve's proof, I don't understand the premise that the chosen bit that a party outputs when the other party aborts is deterministic. Since they are PPTs, and they are notified when the other party abort, can't the honest party just flip a random coin and output that?