Algorithm for Capturing Pokémon
dragonflycave.com
dragonflycave.com
Second generation (Gold, Silver, Crystal): http://www.dragonflycave.com/gen2capture.aspx
Third generation (Ruby, Sapphire, FireRed, LeafGreen, Emerald) and forth generation (Diamond, Pearl, HeartGold, SoulSilver, Platinum): http://www.dragonflycave.com/capture.aspx
For a general overview and comparison of changes, the Bulbapedia page is worth a look: http://bulbapedia.bulbagarden.net/wiki/Catch_rate
Awesome article, but I suspect that something is wrong. If we see Mewtwo, lvl 70, full hp, frozen solid it says that -on average- we need 6 ultra balls. That is FAR from true. I always freezed all the legendaries to capture them easier, and it took always more than 10 balls to capture them.
The process of capturing is a Bernoulli process [0]: each time you throw the ball, there is a P chance of catching it, and it is independent of subsequent throws.
Chance of catching, given 1 ball = P Chance of not-catching, give 1 ball = (1 - P) Chance of not-catching, given 6 balls = (1 - P)^6
For P = 17.5%, the chance that you don't catch your Mewtwo with 6 balls is 31% (which agrees with your observation that it often took more than 6 balls).
Let's try for 10 balls: (1-0.175)^10 = 0.15 (still a 15% chance of not catching it).
It's never certain! Even with 100 balls, there's a very slim chance you won't catch it.
Also, Generation 1 had Nest Balls and Net Balls, didn't it? Those are missing from this list.
So here's a cool question/poll:
What Gameboy hardware did you own?
I had an original Gameboy, a Gameboy camera (no printer), a silver Gameboy pocket, a Gameboy Color, and a red Gameboy Advance SP. The Advance SP was awesome but my roommate in college stole and sold it to buy cigarettes.
I also had a Virtual Boy and an original Nintendo DS.
*Edit: I also had one of those lighted magnifier/speaker rigs for the original Gameboy which meant I could play Metroid after dark and feel like a SPY!
These games could be ported to iOS and Android with minimal changes and still be succesful.
I tried a Final Fantasy for Android and it was decently playable, I was hoping for Final Fantasy Tactics (which according to Wikipedia was released in 2013 but only for Japan), and very especially for a followup. Square Enix seems to be among the very few that do that, I guess Nintendo doesn' want to cannibalize their mobile platform (they're facing a typical Innovator's Dilemma).
Pretty cool nonetheless.
http://tasvideos.org/3767S.html
These are becoming more popular. There's similar ones for later Pokemon games as well as more impressive titles like Super Mario World for the SNES:
Generation 4/5 also had a number of other ways to manipulate another RNG, that basically made capturing high-IV and shiny Pokemons almost trivial. People wrote Windows desktop applications to tell you exactly how many times to flip a coin to get the RNG exactly where you wanted it.
There's a big debate in the Pokecommunity whether or not this is cheating. You can probably figure out both sides big arguments already.
Great, you probably just got me playing again. There goes my free time ;)