There are a few problems with Amazing Initiative. First it breaks the randomness of the d20 roll for initiative with a flat +20 bonus. This is pretty boring and creates a frigid gap between mythic players and non mythic monsters in terms of the opening round of combat.
Secondly, it allows high mythic tier players to essentially take double action a huge number of times in a single combat, which requires a DM to double the number non mythic enemys or to create mythic enemys with Amazing Initiative of their own to compensate. This leads to both sides taking double moves while expending a point each round to be at max efficiency, which is redundant. It essentially creates two rounds with a mythic point drain.
Third, the ability does not address how to handle full round action timelines and becomes sloppy in explaining a course of events.
After some brainstorming I've come up with a rule adjustment to solve all three of these problems:
At 2nd Tier a player may roll an additional d20 during initiative checks and add both rolls along with any other bonuses when determing their initiative score. The higher of these two dice rolls is considered the player's Mythic Initiative Bonus.
Once per combat a player may spend a mythic point at the end of their turn as a free action to take an additional turn that round in the initiative list where they would be without their Mythic Initiative Bonus. Any full round action being performed by the player from the previous turn is completed at the beginning of this additional turn.
At the end of this additional turn the player has two options, they may end their turn and retain this position in the initiative list the following rounds, or choose to spend an additional mythic point and return to their original position in the initiative list before losing their Mythic Initiative Bonus. If the player chooses this second option any full round action they were performing is completed at the beginning of their next turn.
This power cannot be used again until the combat ends and initiative is rolled for a new combat.
Its in the spirit of the original idea but doesn't break the game, and addresses game mechanic holes. It also forces the player to spend additional point to force two full round actions into one round.
What do you guys think?
The solution lies in the power point economy. The campaign needs to have enough encounters per day that the mythic players would run out of power points unless they conserve them.
Don't restrict the use of power points. Let the players choose how they want to spend them. A fun game rewards players for smart play. A DM that nerfs smart play soon has a boring game. Instead, provide more challenges, and more difficult challenges; enough that amazing initiative is no longer a "no-brainer" because the potential depletion of power points is always on their minds.