A helpful visualization, from a past discussion: https://xcancel.com/grantslatton/status/1754912113246798036

That may have been done in the underlying paper by Mitzenmacher et al., but I haven't checked.

I'm more confident that that paper established that firing n requests at n servers will result in a max server load proportional to log(log(n)) with high probability, vs. proportional to log(n) for random -- IOW an exponential improvement in max server load over random.

I think that simulation claim that pick-2 can send 2.5x as much traffic to most loaded vs least loaded is a bit misleading: if the load metric is completely random then that might happen. The more correlation to load the better. Also, rather than looking at the ratio of most loaded to least loaded, it might be better to look at the ratio of most loaded to average: that is, how much extra work did we send to a poor server. In that, pick-2 has an absolute cap of 2xing the load on a server.

Excellent read. It highlights key aspects like health checks, server restarts, warm up, and load shedding, all of which make load balancing an already hard problem even harder.