1. A stateless load balancer, comprising: one or more processors; and memory storing components executable by the one or more processors, the components perform acts comprising: receiving a request that is initiated by a client device, the request being transported to the stateless load balancer via a communication connection; obtaining connection tuples of the communication connection that transported the request, the connection tuples including a source internet protocol (IP) address and at least one of a public destination IP address, a public destination port number, a source port number, and a protocol type; generating a hash value from the connection tuples of the communication connection; mapping the hash value to a private network address of a plurality of private network addresses based on mapping data; routing the request to a computing device of a plurality of computing devices that has the private network address; and returning a result obtained by the computing device performing a task specified in the request to the client device.