When do flamingos stand on one leg?

I was impressed that horses can sleep, standing on four legs.

Tom, They'd have trouble trying to sleep on two, let alone one.

A flock of flamingos is called a flamboyance

YoungAtHeart, that’s why I prefer to just lay the heck down!

It seems counterintuitive that they are more stable on 1 leg which is off-center from their body.