thanks a ton for all the replies guys. sorry i didn't respond to any of you guys for a while.
heres the short little essay thing i wrote to go along with the presentation. i dont know if all of it is right, and i dont claim to be smart at all. thats just what i wrote and i got an A.
Super Smash Bros Melee and Modern Physics
Super Smash Bros Melee (Melee) runs at 60 frames per second. This means that in every second, there are 60 little pictures being meshed together to make one seamless video. Although every time you input something in your controller it feels like the game is responding instantaneously, it’s actually not at all. In fact, every input you ever do will have a completely unique time that it takes for your character to start doing your input.
Frames act as “ticks.” Every tick the game displays new inputs that have been inputted between these ticks. 1 frame is equal to 1/60th of a second, so that means that the time it takes for your character to do your input can range anywhere between 0 and 1/60th of a second ( 0 < x ≤ 1/60th ).
Frame 0 (0 s)
-------- (inputs)
Frame 1 (.0167 s)
-------- (inputs)
Frame 2 (.0333 s)
This may not seem significant, but theoretically this could determine the outcome of a match! And not only that, but it also could determine a winner by pure chance!
Take, for instance, Fox and Falco’s “shine” (hold down + B). Shine is the fastest move to come out in the entire game. Its “hitbox” (the area in which it hits people) comes out on the first available frame that you input the move. So how could this determine a winner by chance? Take these 2 situations:
Situation 1: A Fox and a Falco are on the edge of Dreamland. The game is tied at one stock apiece, and both characters are at high enough percent to where a shine hit from either will certainly lead to death. The Falco has his back towards the edge of the stage, and the Fox is facing the edge.
_______________X_Y (X = Fox, Y = Falco)
Now lets say that the Fox inputs his shine at t = .0180 s, and the Falco inputs his shine at t = .0280 s. Even though there is a 1/100th of a second difference, the two moves will show up on the game at the same time (both .180 and .280 are after .0167 and before .0333, so they will be displayed in the game on .0333). The moves will “clank,” and neither player will get hit. The game goes on.
Situation 2: Picture the exact same situation before, but this time, the Fox inputs his shine at t = .280, and the Falco inputs his shine at t = .380 s. Although the two players have still inputted their moves with only 1/100th of a second of a difference, these moves will appear on different frames. In fact, Falco’s shine won’t even come out! He will have already been plummeting to his death because of Fox’s shine.
Given only the difference of time that the 2 moves were inputted, you can actually calculate the probability that the moves will come NOT out on the same frame using this equation:
(Tinput1 – Tinput2)/(1/fmedium)
Where T is the time of each respective input and fmedium is the frame rate of the game being played (in this case, 60 frames per second).
As you can see, at its absolute base level, a melee match can certainly be determined by luck and probability. Although this isn’t truly random like quantum mechanics, for two players sitting down and playing a match this IS random. It would be impossible for players to account for this during a game. We as human beings simply cannot process time at that small of a level.
So how can we possibility eliminate this game of chance? The only way to do this would be to make the frame rate
infinity frames per second. In other words, every input you do would happen on screen at the
exact moment in time you inputted it.
(Tinput1 - Tinput2)/(1/
) =
IFF (Tinput1 - Tinput2)
0
EDIT: ah^^ those didnt work
. in words, the equation is supposed to be: the limit as f approaches infinity of Tinput1 - Tinput2 divided by 1/infinity is equal to infinity if and only if Tinput1- Tinput2 does not equal 0).
There are two uncertainties with this equation, however. Firstly, would two people be able to ever input anything at the
exact same moment in time? There are infinitely many decimals for any moment in time, so would it even be possible? Secondly, and more importantly, is an infinite frame rate even attainable? At that point would the game actually become reality? (disclaimer: the time it takes for the controller to send the message to the game does NOT affect this. Assuming the time is constant for every controller, all it would do is add a C value to each Tinput, which would then cancel out).
EDIT: all the subscripts and some other stuff didnt come out clearly. i copied and pasted it from my word doc. sorry
