Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. A mutual exclusion algorithm is adaptive to point contention, if its RMR complexity is a function of the maximum number of processes concurrently executing their entry, critical, or exit section. In the best prior art deterministic adaptive mutual exclusion algorithm, presented by Kim and Anderson [22], a process performs O min(k, log N) RMRs as it enters and exits its critical section, where k is point contention and N is the number of processes in the system. Kim and Anderson also proved that a deterministic algorithm with o(k) RMR complexity does not exist [21]. However, they describe a randomized mutual exclusion algorithm that has O(log k) expected RMR complexity against an oblivious adversary. All these results apply for algorithms that use only atomic read and write operations. We presen...