As a promising solution for handling super dense wireless networks, wireless local area networks (WLANs) have been intensively considered due to their wide availability. However, the contention-based MAC protocol in WLANs should be modified because of its inefficiency. To this end, we consider a recently proposed novel MAC protocol called the renewal access protocol (RAP). With the RAP, we analyze two strategies for resolving collisions efficiently and achieving optimal throughput performance in super dense WLANs: strategies without and with grouping. First, we analyze the asymptotic behavior of the RAP itself (i.e., without grouping) as the number of terminals goes to infinity. We show that the RAP can achieve optimal throughput even in super dense WLANs and the relevant optimal access probability can be derived in a closed form. Second, we propose a grouping strategy in the RAP called the grouped RAP (G-RAP). While a grouping strategy in the IEEE 802.11ah standard is based on time division, our G-RAP is based on transmission attempts. So the G-RAP does not waste channel resources. We show that the G-RAP achieves the optimal network throughput for any group structure if terminals use the optimal access probability that we derive. Our analytical results are validated by simulation.