"Your chance at the perfect pokemon (100% IV, right moveset)"

#PokemonGO: I see a lot of people here looking for the perfect pokemon, the one with 100% IV and the right moveset. I did that myself for a little while, until I decided to break down the actual probability to get such a pokemon.There is 3 hidden values with the IV: Attack, Defence and Stamina, and all of them are given a random value between 0 and 15 included, hence 16 possibilities each.Now, the perfect IV is 15, 15, 15. If all three values are random, your chance to catch a given pokemon, let's say a Dratini, with those stats is (1/16)(1/16)(1/16) = 1/4096. So, for a specific specie, you have one chance in 4096 to have the perfect IV.But, as many will already know, having the perfect IV isn't sufficient. You still need to have the right moveset. Let's take the popular Dragonite as an example: Dragonite has 2 possible main attack, and 3 possible charged attack. Moveset is chosen at random when you capture or evolve. Hence, your probability to have a Dragonite with the right moveset is (1/2)*(1/3) = 1/6. You have one chance on six to get a Dragonite with the right moveset.So, what's your shot at a Dragonite with the right moveset and perfect IV? Easy, that's (1/6)*(1/4096) = 1/24576! That's right, you read correctly. You have one chance on twenty-four thousands five hundreds and seventy-six to get the perfect IV Dragonite with the moveset you want! And as, like stated before, the movest changes when evolving, hence there is no guarantee that evolving a perfect Dratini with the right moveset will end-up in the best possible Dragonite, since the moves can change.This is of course applicable to other pokemons too, you just have to adapt a bit as some have more or less options with the moveset.Now, if you want to hunt dratinis and its evolutions until you get that 1 in 24576 that's up to you, but quite frankly, you should be perfectly happy with your 85% Dragonite that has the right moves.Edit: As it was kindly mentionned by pyroclasm404, Dratini evolution tree is a bad example as Attack will always be maxed at 15. Hence, for the perfect IV Dragonite, your chances are actually way better, with 1 in 256. There's still the moveset to take into account though, which depending on if you're set on either attack or defence will take this to 1 chance in 1536, and if you don't care to in chance in 768.Edit2: It seems that the "granted" max stat isn't so granted after all: I just caught a Dratini 309cp, 46hp, 1600dust to level. The sheet gives me only 2 possibilities for this Pokemon: LVL 13, 0/5/14 LVL 13, 0/4/15 with stat given in the order: ATK/DEF/STA, hence I just caught a Dratini with 0 bonus in ATK.Edit3: Chance to get "a perfect pokemon" from an egg is higher. Chance to get "a perfect pokemon from this exact specie" from an egg is lower, because you need to consider the egg's probability to give you the pokemon you want.Edit4: If the distribution is random, the chance of 0%, without considering eggs, is the same as chance of 100%. If you consider eggs, then chance of 0% is lower.Edit5: If the distribution is random, the average IV is 50% for a pokemon caught in the wild. It's 83% perfect in average for eggs if random and min from eggs is 10-10-10. via /r/TheSilphRoad http://ift.tt/2afVQx8