In this paper, we propose some improvements to the flooding protocols that aim to efficiently broadcast a given information through the whole ad-hoc network. These improve-ments are based on probabilistic approach and decrease the number of emitted packets and hence, the medium occupation. Indeed, it is more interesting to privilege the re-transmission by nodes that are located at the radio border of the sender. We observe that the distance between two nodes with full duplex communication can be approximated by comparing their neighbor lists. This leads to broadcasting schemes that do not require position or signal strength information of nodes. Moreover, proposed broadcast protocols require only knowledge of one hop neighborhood and thus need only short hello message. Such protocols are more able to support high mobility networks than protocols that need knowledge of two or more hops neighborhood and then need longer hello messages. We compare our new schemes with variable density and experiments show that the probabilistic approach is efficient.