Now this is rather tedious and lengthy, so I'll try to keep it simple =)
Let me start off by explaining how a shiny pokemon is determined in the first place, just to give you a better understanding.
Everyone has a 16-bit ID number and a hidden 16-bit ID number in their game. Sixteen bits means that it can be any decimal number from 0 to 65535, so it's not possible to get an ID number that starts with a 7, 8 or 9.
A bitwise XOR is performed on these ID numbers to get a sixteen-bit combined ID number.
[Jesus, I'll have to explain binary now. I'll put it at the end of the post.]
Suppose my ID number is 12181. In binary this is written as 0010111110010101.
Now suppose my hidden ID number is 50396. In binary this is written as 1100010011011100.
Now let's perform a bitwise XOR on these numbers to get our combined ID number.
0010111110010101 XOR
1100010011011100
1110101101001001
OK, so our combined sixteen-bit ID number is 1110101101001001 (which is 60233 as a decimal number).
When you encounter a pokemon a 32-bit Personality Value is randomly generated. Well, half of it is randomly generated; the other half is your combined ID number.
So suppose the second half, the randomly generated half, of our 32-bit Personality Value is 0110100011010101 (which is 26837 as a decimal number).
So now our Personality Value is 1110101101001001 0110100011010101.
Now we split this in half and do a bitwise XOR on the two 16-bit numbers.
1110101101001001
0110100011010101
1000001110011100
OK, and 1000001110011100 is our Shiny Value. If this value comes out to be less than 8, our pokemon is shiny.
Now let's see, our shiny value is 33692 so our pokemon is in fact…not shiny. Well what were the chances, eh? lol
Since this shiny value can be any decimal number between 0 and 65535, our probability of encountering a shiny pokemon is 8/65536, which is the same as 1/8192.
Now, you're probably wondering what this has to do with chaining. Every time you chain a pokemon the probability of getting a shiny increases, right?
Well when you've got a chain going, the second half of the personality value, the randomly generated part, is either restricted so that there are fewer possible outcomes that the shiny value can have or the probability of the shiny value being less than 8 is increased. This rate goes according to the exponential curve on the graph I showed you earlier. I don't know exactly which numbers the game restricts or exactly how, to be perfectly honest. I just know that –
Either (i) they are restricted; or
(ii) the probability of the shiny value being less than 8 is increased.
I honestly don't know which one it is because I still haven't worked it out (I need to do some more research). One way to find out will be to chain several Wurmple or Spinda on one person's game and see if all the shinies have any similarities.
If most of the shiny Wurmple seem to only evolve into one form, this shows us that the randomly generated personality values are restricted. This is also the case if the shiny Spinda seem to have spots in the same places. You can also find out what else personality values are used for and compare your shiny pokemon. I think gender, nature and ability are determined by personality value too. Personally I think (ii) is the one but I may very well be wrong. I wouldn't know because I don't chain. And let me say this again: I need to do some more research on this.
So, with our combined ID number of 1110101101001001 (60233), the game works out which randomly generated numbers are the ones which make our pokemon shiny.
I worked these out for our ID number and the randomly generated personality values need to be:
(0) 1110101101001001
(1) 1110101101001000
(2) 1110101101001011
(3) 1110101101001010
(4) 1110101101001101
(5) 1110101101001100
(6) 1110101101001111
(7) 1110101101001110
You may be wondering: if a different player with a different combined ID number had one of these randomly generated personality values, would the pokemon be shiny for both players? And the answer is no. These numbers need to be different for every possible combined ID number. So a wild shiny pokemon with one of these random values on my game would probably not have been shiny if you had run into it in the wild.
By the way, please don't outright criticize me about this, I'm only trying to help and I'm only stating what I've worked out so far. I don't know
everything about it! I'm so sick of having people criticize me and question my intelligence all the time...
To briefly explain binary
To convert a decimal number into a binary number you can draw out a table to help you.
This is what you need for a 16-bit ID number, or a number between 0 and 65535:
Now let's work out what 12181 would be in binary in steps.
We start off with 12181 and we work across the table from left to right. We need to subtract the largest possible number from 12181 without going over and put a 1 in its place on the table.
The largest number we can subtract from 12181 without going over is 8192 so we put a 1 in the position of 8192.
12181 - 8192 = 3989 so the next largest number we can subtract from that is 2048 and we put a 1 in there.
3989 – 2048 = 1941 so the next largest number we can subtract from that is 1024 and we put a 1 in there.
1941 – 1024 = 917 so the next largest number we can subtract from that is 512 and we put a 1 in there. Anyway, it keeps going on like that until you get your number down to zero.
So for 12181 our table ends up looking like:
And all we need to do now is put zeros in the blank spaces, so we have:
There we have 12181 as a binary number:
0010111110010101
See, it's actually really simple isn't it?
Now to explain what I mean by "bitwise XOR"
The binary XOR operation stands for "exclusive OR"
Basically, when you have two binary numbers and you perform a bitwise XOR on them you use this Boolean logic (I hope I spelt that right):
0 XOR 0 = 0
0 XOR 1 = 1
1 XOR 0 = 1
1 XOR 1 = 0
If you look back at the way I performed XOR on the binary numbers, you look at the vertical pairs of numbers individually and do the XOR on only two numbers at a time. That's what the "bitwise" part means.
So we can take:
0010111110010101 XOR
1100010011011100
and we get:
1110101101001001
I wrote it above as:
0010111110010101 XOR
1100010011011100
1110101101001001
Hopefully I explained that OK.
hmmmmmmmm
but isnt 1/200 is the max you can go in catching a shiny??
if you do get 100 chains or more what would be the probablity of that??
wouldnt it still be the same?
I'm pretty sure 1/200 is the max you can get.
If you want me to try and calculate the probability of getting a shiny with a chain of 100 using the shiny formula then I'll do it but it's not going to make any sense.
Umm…well my calculator is really ancient and it can't cope with some of the numbers, so I'll just do approximate values (and I left it at college >.<).
So if you want to ignore the fact that with a chain of 40 you get your highest probability, then apparently:
With a chain of 41 your probability of getting a shiny is 1/0 (in other words, infinity)
With a chain of 80 your probability of getting a shiny is about -1/7800
With a chain of 100 your probability of getting a shiny is about -1/11800
See what I mean? If you start using numbers outside the range you start getting ridiculous, impossible probabilities. A probability can only be a value between 0 and 1! I even feel silly writing those false ones in.
But then again, I could be making a gigantic mistake here and
ShadowTails could in fact have the correct theory and even though it
seems to makes sense, all that binary could actually be a load of rubbish :P nah, don't worry my binary is definitely correct :laugh:
But yeah, I do see what you mean,
ShadowTails. I don't actually know for certain that
any of it is correct because there aren't any sources of information on this. I mean, it's not exactly common knowledge, is it? It's just a question of working it out, I guess.
hey i was wondering how do you improve your chances of seeing a shiny in ruby/saphire/emerald or fire red/leaf green??i dont think you cant but if there is can someone tell me??or is just pure luck like 1/8000something like that?
Sorry to tell you this, but I don't think there is any way you can increase your chances of getting a shiny on those games, it's still a 1/8192.
But I'll let you in on something: you know how each of those Unown ruins contains a different letter Unown? I think some players are more likely than others to get a certain letter Unown shiny ;)
But that doesn't really help you to get one, seeing as you don't know what your hidden ID number is…
Well, I hope all of that made some sense to you all :\