Luck Manipulation
Luck manipulation is the act of using
savestates / calculations to predict
how the game would react to different input,
and then choose the input that leads to the most
desirable result in a particular situation.
It is also called "luck abuse", "randomness abuse" or "controlling randomness".
Background
In computer games, "luck" is determined by mathematical algorithms
that use the player as their entropy source.
There is no real randomness, but only an algorithm
(a sequence of mathematical instructions) that permutates
an entropy source (the timer and the player's input) to
produce a chaotically changing sequence of numbers. That
sequence will be used as the source of random numbers for
all purposes of the game.
In Mega Man 2, the entropy comes from the horizontal positioning of Megaman.
By moving at different speeds (walking and jumping are different speeds to start),
one can manipulate the behavior of everything that is supposedly random:
- drops from killed enemies;
- enemies' decisions (whether to shoot or to jump, whether to move up or down…).
Some decisions by the enemies are simply deterministic: they depend on the
position of Megaman in relation to the enemy, or they react to shooting, etc.
Others depend on the randomness.
Of course, it is normally impossible to predict
how exactly the randomness will be changed with the different maneuvers, since even a difference of 1 frame (1/60 of a second) in timing can affect the subsequent events, and the changes are chaotic (
http://en.wikipedia.org/wiki/Chaos_theory).
That's why it is called "random".
To predict it, one needs a computer to simulate the algorithm to see which
input gives the desired result. This is what rerecording enables us to do.
Instructions 
Learning to abuse the determinability of randomness is very useful in making of TAS movies.
You can affect anything that has an element of randomness in it,
such as enemy movements or item drops, simply by giving the game different input:
- which buttons you press, and
- when you press them.
Another thing to be aware of is when particular outcomes are decided.
For example, depending on the game, what item an enemy is destined to
drop could be determined:
- at the moment of entering the scene or the moment the enemy spawns;
- at the moment you kill the enemy;
- at the moment the leftover item or its holder (e.g. a treasure chest) appears;
- at the moment the holder is opened.
This means that in some games you can affect item drops by doing different
motions as an enemy dies, or by killing the enemy earlier or later, while in
other games you have to experiment by entering the room at different
times or even from different angles.
Picture on the right is an example of shooting the same enemy at a slightly different time in NES game Darkwing Duck.¶
One of the prime examples of luck manipulation is the
Dragon Warrior movie. The player abuses luck in his movie of this game in different ways.
- All undesired enemy encounters are avoided by stopping his motion for a frame or two at various times along the player's path.
- When encountering enemy, its HP is manipulated to be as low as possible.
- Critical hits are gotten 100% of the time by scrolling through the battle menu and waiting to attack on a particular frame. A single frame of difference would not have resulted in a critical hit.
- When using an enemy encounter to suicide, the enemy is manipulated to attack first.
Luck manipulation is possible on a real console, but certainly not to such great extent. Basically, in vast majority of cases the unassisted player is forced to redo major sections of the run, or the entire run if it's done in one sitting (akin to rerecording, but on a much larger scale), until they get an outcome or a sum of them they are satisfied with. Perfect luck is usually practically unattainable, nor expected in unassisted speedruns.
On the contrary, a TAS player is expected to attain the best possible result, or at least be only negligibly far from it, which sometimes requires having a deep understanding of the game's inner workings through means of
memory search or ROM disassembling.
More reading