Broadcasting is an elementary operation in wireless multi-hop networks. Flooding is a simple broadcast protocol but it frequently causes serious redundancy, contention and collisions. Probability based methods are promising because they can reduce broadcast messages without additional hardware and control packets. In this paper, the counter-based scheme which is one of the probability based methods is focused on as a broadcast protocol, and the RAD (Random Assessment Delay) Extension is proposed to improve the original counter-based scheme. The RAD Extension can be implemented without additional hardware, so that the strength of the counter-based scheme can be preserved. In addition, we propose the additional algorithm called Hop Count Aware RAD Extension to establish shorter path from the source node. Simulation results show that both of the RAD Extension and the Hop Count Aware RAD Extension reduce the number of retransmitting nodes by about 10% compared with the original scheme. Furthermore, the Hop Count Aware RAD Extension can establish almost the same path length as the counter-based scheme.