We consider open addressing hashing, and implement it by using the Robin Hood strategy, that is, in case of collision, the element that has traveled the furthest can stay in the slot. We hash #n elements into a table of size n where each probe is independent and uniformly distributed over the table, and # < 1 is a constant. Let Mn be the maximum search time for any of the elements in the table. We show that with probability tending to one, Mn [log 2 log n + #, log 2 log n + # ] for some constants #, # depending upon # only. This is an exponential improvement over the maximum search time in case of the standard FCFS (first come first served) collision strategy, and virtually matches the performance of multiple choice hash methods.