Round 1: Fight to the death near The Tree (which exists in both Mythos).
Round 2: The main battle is in the ocean, with Azathoth and the Scarlet King fight in a pocket dimension.
Round 3: Finish of Round 2, Whoever won the fight between Azathoth and the Scarlet King absorbed the other one (including their intelligence and malevolence), The Ambassador and Nyarlathotep are now the same being, and Cthulhu and the Great old ones have been summoned all of which are attacking the Scarlet King/Azathoth, The foundation arrives after 2 hours.
The Ambassador is helping the battle and the Hanged Kings stays on the sidelines unless he is killed, the battles can last for as long as needed as well.
Bonus round: The respective cults of the Outer g Gods and the Old Gods, are in a death match In a empty field who wins?submitted by /u/StatistUnion