User wants perfect 'Round Robin' load distribution

I would suggest Least Connections would actually be better.

What you have to remember with Round Robin is that it doesn't take into account the length of a session. So, lets say you had three servers. Connection 1 to server 1 lasts 30 seconds, connection 2 to server 2 lasts 10 minutes, connection 3 to server three lasts 5. Connection 4 to server 1 lasts 29 seconds. Connection 5 to server 2 lasts 3 minutes.

After 1 minute server 1 has 0 connections, server 2 has 2, server 3 has 1.

Keep going and you can see how things get all uneven.