Pirate A picks out what he thinks is a third of the loot. Pirates B and C, in turn, have the option of returning some of it to the chest. In effect, each is making a bid as to the smallest “third” that he’s willing to accept. The last one to make a proposal (which might be Pirate A himself) keeps this first portion for himself. The other two pirates then split the remaining treasure in the conventional way: one divides it into two portions and the other chooses between them.