No Refills Low% analysis

NoRefills-Low% analysis (for PAL and NTSC, inbounds, without SpaceTime-beam):

Definition:

It is not allowed to collect any kinds of drops and no refill-stations nor the ship are allowed to be used, such that the only ammunition is given directly by collecting items. The only exception is at the very end by obtaining health via the big Metroid during the fight against MotherBrain. Crystal Flashes are allowed (but I doubt they will be helpful in the end).

A rough estimate gives an upper bound of 23% for PAL (for TAS) and 14% is a general lower bound, but further optimization and reasoning still needs to be done.

Constraints to generate a better lower bound for the necessary number of items (for TAS):

5 Missiles are needed at least to open Bomb Torizo´s door

5 Missiles are needed at least to open the door for either early SuperMissiles or Sporespawn´s SuperMissiles

1 projectile is needed for entering the pre-golden-statues-room

1 projectile is needed to enter Dachora´s room

1 projectile is needed for the Charge-room door at the bottom right side

1 projectile is needed for the door on the right side in Noob-Bridge-room

2 projectiles are needed for the SuperMissile block at the entrance to Kraid´s Lair

1 projectile is needed for Kraid´s Eye-door

1 projectile is needed for Phantoon´s Eye-door

1 projectile is needed for either the left entrance-door to Wrecked Ship or Ice is needed, so it would be needed for either the entrance-door to Ice-beam´s area or for the entrance-door to Speedbooster´s area (or for Crystal Flash...)

1 projectile is needed for the door leading to pre-Draygon-room

1 projectile is needed for Draygon´s Eye-door

1 projectile is needed for the door leading to the ninja-pirate´s room

18 projectiles are needed for killing MotherBrain 1

1 projectile is needed for the door leading to MotherBrain´s Eye-door room

1 projectile is needed for MotherBrain´s Eye-door

Summing all of this up, we get already 10 Missiles and 31 SuperMissiles neglecting potential ammunition for zebetites and potential ammunition to get the SuperMissile packs. Hence at least 2 Missile packs and ammunition that corresponds to 7 SuperMissile packs is needed. Comparing this to what can at most be gotten in any 14%category, the difference of packs is at least 5, hence a lower bound for NoRefills-Low% is (14+5)%=19% (for both versions).

If any Crystal Flashes were used, then at least 5 more items would be needed (for 10 Missiles, 10 SuperMissiles and at least 5 more powerbombs, considering one has at most 10 powerbombs in a low%category and has to use 1 powerbomb for entering the lavapit, 1 for entering Ridley-PB-room aswell as 2 for the statue in that room) which would lead to 24%.

Now, in order to prove that no CF can be included in an optimal NoRefills-Low% option, one shall find explicit routes for upper bounds of number of items needed.

[TODO: Find complete set of optimal solutions for TAS and for humans.]

[Sidenote: NoRefills-Max% is actually 100% and easily humanly doable.]