The design of an efficient Medium Access Control (MAC) is challenging in ad-hoc networks where users can enter, leave or move inside the network without any need for prior configuration. Chlamtac and Farago have proposed a topology unaware TDMA-based scheme, suitable for ad-hoc networks, while Ju and Li have proposed an enhanced version that maximizes the minimum guaranteed throughput. Both approaches consider a deterministic policy for the utilization of the assigned scheduling time slots. In this work it is shown that this deterministic policy fails to utilize non-assigned slots that would result in collision-free transmissions even under heavy traffic conditions. A simple probabilistic policy is proposed, capable of utilizing the non-assigned slots according to an access probability, fixed for all users in the network. An analytical study establishes the conditions under which the probability of success for a specific transmission under the probabilistic policy, is higher than th...