Sorry for bumping an old thread, but I happen to collect shinies and I can share some info on how to soft-reset for them intelligently.
You can calculate the probabilities of encountering a shiny Pokémon after a given number of resets using powers and logarithms, and then use that to plan a schedule.
(MATH WARNING)
An easier way of calculating probability in this case is to calculate the chances of the event not happening. For every wild Pokémon you encounter/receive in your game, there is a 8191/8192 chance of it being not shiny. If you're going to reset several times, you can then raise that value to a power, and subtract the answer from 1 in order to get the chances of any one of those resets coming up as shiny.
For example, let's say we're going to reset one hundred times.
(8191/8192)^100 = 0.987866 chance that none of the resets will come up as shiny
1-0.98766= 0.01234, so it's about a 1.2% chance of getting a shiny after only 100 resets.
Now, this might seem better at first, but if you graph an exponential function like this, you'll see that the value you'll get will never reach 0. It approaches 0, but never reaches it. There is no number of resets that will give you a guaranteed shiny.
Let's try plugging in a different number Shadow gave the example of 10,000, so let's use that.
1-(8191/8192)^100=0.70500
That's just more than a 70% chance. Shadow's friend was unlucky, but not extraordinarily so.
You can try plugging in all the values you like, but sometimes it can be helpful to calculate the exact number of resets needed to have a certain chance of getting a shiny. For that, we need to use logs. For those of you who haven't had advanced algebra yet, log functions are basically reverse-exponents. We want to take the log, base 8191/8192, of the target probability to get our number of resets.
Here's a formula you can plug into a scientific calculator, even if you don't get how it works:
(ln(1-P)/ln(8191/8192)) = R
P = probability of getting a shiny
R = resets required
We're using 1-P because we're still technically calculating the probability of none of the resets being shiny. You'll probably get a decimal number, which you'd want to round up because you can't do .2 of a reset.
Say you want to know how many resets will give you a 90% of getting a shiny:
ln(0.1)/ln(8191/8192) = 18862
PEARL OF PALKIA! THAT'S A LOT OF RESETS! How are we ever going to fit that many resets into our schedule?
First of all, you want to learn how to multitask while resetting. Streamline your process so that you're hitting A habitually at the right times, and that you hit L+R+Start+Select right when you get a good look at the Pokémon. You can reset while doing anything that doesn't require both hands or your full attention. Browsing the internet, IMing, watching videos, and daydreaming are things that I frequently reset while doing.
Secondly, you're obviously not going to be doing all these resets in one day, so I'd recommend making a schedule for it. 100-200 for school days (if you're in school) and 500-800 for weekends/breaks is what I'd recommend. Yes, that's a lot of time, but you really want that shiny, don't you? Calculating the probability as above can give you a good idea when you'll get that shiny if you keep to your schedule, though it truly is random and your chances don't ever improve. I keep track of my resets by making tick marks on a sheet of scrap paper. Pretend you win something for having a record of so many resets that will keep you going when tedium sets in.
I hope this makes things a little clearer regarding probability and actually doing this while remaining productive/sane.
(written and posted while resetting for a shiny Toys R Us Arceus in Platinum)
