Your formula is incorrect.

Your error is that each soft reset, you actually get three tries for a shiny.

This is because if a pokemon is shiny, the preview sprite will be shiny. That is, you can tell that it is shiny before you actually select it.

The actual solution is a geometric distribution.

The probability of getting no shinies in one soft reset is the probability of the first one not being shiny, times the probability of the second one not being shiny, times the probability of the third one not being shiny, or: (8191/8192)^3.

The probability then, of getting at least one shiny in one soft reset is 1-(8191/8192)^3.

Let x be the number of SRs. Then the probability of getting at least one shiny in x or less tries is

1-(8191/8192)^(3*x)

If we want a 50% chance of finding a shiny, then we need 0.5 = 1 - (8191/9192)^(3*x)

solving for x we get

(log(0.5)/log(8191/8192))*(1/3) = x.

That is, x = 1892.638568.

In order to have a better than not chance of getting a shiny, you need to do 1893 soft resets, not 4096.

If you can do 3 soft resets in 1 minute, then you can do 180 soft resets per hour. Then it will take you approximately 10.5 hours to have a better than not chance of finding a shiny.

To have a 99% chance of finding a shiny,

(log(0.01)/log(8191/8192))*(1/3) = 12574.41847

you need 12575 tries, which, at 3 soft resets per minute, will take you about 70 hours.

Every year, the French say that Lance Armstrong is on chemicals. It's chemotherapy you toadsuckers! - Robin Williams