I use a 50 foot rope to pull my sled when on sketchy ice. I for sure don't want to worry about my gear when I go in. If I have a buddy, we stay that far apart, and hold on to the rope so we won't have to throw it if one or the other goes through.
Another good thing about taking a buddy- chances of 2 people having bad judgement at the same time are very low. One or the other of us has always chickened out before we fell in.
Alone, my record is not perfect...
Maybe it is just me