A processing device can implement an optimal fair distribution. In one embodiment, the processing device divides a distribution pattern associated with a distributed system into segments based on a quality of distribution for the distributed system. For each partition of the plurality of partitions, the processing device calculates a weight for the partition based on a number of segments in the plurality of segments and a capacity of a bucket associated with the partition. The processing device generates a map of partitions based on the weight for each of the plurality of partitions. The processing device distributes a plurality of objects in the distributed system to the plurality of buckets based on the map of partitions.