Trust me, I try to convince folks NOT to use this flipping method for the reasons listed above. I prefer playing cards by far. The reason for this thread was not to discover a better way to choose groups. I already know many.
The goal of this thread was to:
1. Identify possible flaws in the method of flipping in principle AND in practice. (i.e. larger groups flip slower, thus round 3 for this group might happen during round 5 for that group; further complicating the odd-man out solutions)
2. Organize these possible flaws into a neat package that can be easily explained to people who believe the system to be perfect.
[. . .]I've done disc flipping many times and never once had a single bit of confusion.
I think this is due to no one realizing there is a non-random element to this flipping method. Everything is not complicated when you do not observe carefully.
When there becomes an odd man out, they always seem to wander around until they stumble upon another odd man out; then they join up to form a twosome. Unfortunately, this is usually based on physical proximity and not which odd-man is closest to themselves in the branches of the flipping-tree.
If there's an odd man out you just pair them with the next odd man out, not all that complicated.
This rule does not cover half of the possible scenarios. Consider this one:
Round N: In one of the resulting groupings, suppose there is a single odd-man-out.
Round N+1: In one of the resulting groupings, there are two odd-men-out.
Using your "next odd man out" rule, would the odd-man from round N get grouped with the first odd-man from round N+1, based on whoever's grouping flipped fastest? This means someone could game the system by speeding up or slowing down their grouping's flips depending on the attractiveness of the odd-man-in-waiting.
In another scenario, what if round N has 3 odd-men out? Are we to determine who's disc landed first and second?
Regardless, once the field of players splits into 5+ groupings, there's no reasonable expectation for all players to flip at the same time, or for all players to keep track of which odd-man came from which branch of the rapidly-dividing field of players.
It's certainly uncomplicated to match up odd-men, if you just gravitate towards the crowd of people you want to group with, then wait for any of them to become an odd-man and call out "Partners!".