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The chance of getting IV31 for every stat would be 1 in 31^6, which equals 1 in 887503681. Add that to the 25 possible natures and you've got a chance of 1 in 22187659525. Multiply that by two in case the Pokemon has 2 abilities and you get 44375319050. Want male instead of female, or the vice versa? Another x2 which brings it up to 88750638100. And finally, if you like the shiny variation more, the grand total would be 1 in 727045227315200. Pokegen? 1 in 1. That's quite a large difference, to say the least.
You aren't going to tell me that you'll actually sit there and go through 727045227315200 eggs just for a Pokemon of your choice, especially when Pokegen exists, would you?
>but anon, I don't need the perfect Pokemon
Oh yes you will, since almost everyone else who plays the game competitively does, and you'd be at a major disadvantage.
>but anon, why not just ban IV manipulation
Because then someone with one team could beat someone else with the same exact team simply based on invisible randomly generated numbers. That's not much of a fair match, is it? Since IVs exist, we've got to work around them, and, at the moment, Pokegen is the only way we can do it("we" being logical, sane human beings that don't want to waste their time with something so viciously tedious).
