Described is a probabilistic concurrency testing mechanism for testing a concurrent software program that provides a probabilistic guarantee of finding any concurrent software bug at or below a bug depth (that corresponds to a complexity level for finding the bug). A scheduler/algorithm inserts priority lowering points into the code and runs the highest priority thread based upon initially randomly distributed priorities. When that thread reaches a priority lowering point, its priority is lowered to a value associated (e.g., by random distribution) with that priority lowering point, whereby a different thread now has the currently highest priority. That thread is run until its priority is similarly lowered, and so on, whereby all schedules needed to find a concurrency bug are run.