Expanding on Mega-Blade X’s answer, using “number of attempts / denominator of odds” is an okay shorthand formula for calculating the cumulative chance if the number of attempts is way less than the odds, but starts getting further from the truth the more attempts you do. The actual formula is (1 - (inverse odds)^(number of attempts)). So, for Gen 4 full odds, that’s (1 - (8191/8192)^(attempts)). Then if you want it as a percentage, you’d multiply it by 100%.
Using the actual formula and plugging Mega-Blade’s calculated attempts of 1920, we get (1-(8191/8192)^1920), which gives us a final true chance of 20.8946% chance of having found a shiny.
