3 points or 4 for alignment

[RiverRunner]

Hello,
I am trying to align my point clouds as accurately as possible. What is the difference between using 3 vs 4 equivalent points for cloud alignment. I see questions regarding both but I don't know what the difference is. Older versions of CC seem to require minimum of 3 while new versions seem to require 4 but still work with 3. I get lower RMS with 3 but should I be using 4?
Thanks

[daniel]

The more the better. It increases the confidence in the final registration, by reducing the impact of a bad pair.

By the way, you can pick more than 4 pairs.

[RiverRunner]

How is that increased confidence defined? I get an RMS with 3, 4, or 8 points. Is there a way to show or express the increased confidence with the more points I have?

[daniel]

Well, not really, apart that the RMS should maybe decrease with the more points you add...