Here is the problem:
When choosing 2 teams from a group of 4 players we start with each player flipping a coin. The first flip could be all tails (a goocher) or all heads (a moon), this occurs 12.5% of the time and requires a reflip. After the first flip, if there is a 3ofakind (odds 50%), then those three continue to flip till two are paired up (odds 75%). During this convoluted choosing process there are two possibilities of entering into an infinite unending succession of flips. This process requires at least 4 coin flips, the odds of resolution with the first attempt is only 37.5%.
1) Is there a simpler process to make the choice? Criteria:

The odds of each team combination being equal

No possible infinite successions

The minimum amount of flips
2) There is a way to decide the teams fairly with one toss, what is it? (There is a hint within the question.)
