"[Analysis] How many 7km eggs do I need to hatch to get all the regionals?"

#PokemonGO: Hi all,It's been a while since I last posted here, but decided last night that I wanted to share with you the number of eggs you need to hatch in order to "guarantee" (to a certain percentage) at least 1 of each regional.Based on the infographic posted yesterday, we see that the egg hatch rates are estimated to be:PokemonEgg Hatch RateFarfetch'd0.0225Mr. Mime0.0225Kangaskhan0.04Tauros0.04Tangela0.0625Porygon0.0625Alolan0.75MethodologyI was going to use some combinatorics to figure out how many eggs you would need to hatch to have a ~50% chance of getting all 4 regionals, but it became too complicated for me when dealing with more than 2 regionals at a time.To figure out the chances of getting 1 specific regional, all you have to do is use the simple formula:1-(1-P(regional))nwhere P(regional) is the probability of the Pokemon (e.g. Mr. Mime) and n is the number of eggs (e.g. 31).Ex: 1-(1-0.0225)31 = 50.6% chance you will get at least 1 Mr. Mime after 31 hatches.For combinations of regionals, I decided it would be a lot easier to write a quick python script and run some simulations (100,000 for each combination of regionals).ResultsHere are the number of approximate number of eggs you need to hatch in order to have an X percentage chance of obtaining at least 1 of each specified regional.Regional Pokemon Combination5%10%25%50%75%90%95%Kangaskhan + Tauros7101730507391Mr. Mime + Kangaskhan913234270107136Farfetch'd + Mr. Mime1217315488131161Mr. Mime + Kangaskhan + Tauros1520314976111139Farf + Mr. Mime + Kangaskhan1824376092133163Farf + Mr. Mime + Kangaskhan + Tauros2228426495135164If you don't see the regional combination below, simply replace a Pokemon with the same egg hatch rate (ex: Mr. Mime + Kangaskhan = Mr. Mime + Tauros, for all those from Australia).How to read:Choose a regional pokemon combination (first column)Choose a percentage chance from the header rowFind the number of eggs you need to hatch.ConclusionTo have a 50% chance of getting the regionals (assuming you have Farfetch'd from a previous global event):If you're from NA (or AU): You need to hatch about 42 eggs to get Mr. Mime and Kangaskhan (or Mr. Mime and Tauros) (14 incubator purchases)If you're from EU: You need to hatch about 30 eggs to get Tauros and Kangaskhan (10 incubator purchases)If you're from SEA: You need to hatch about 49 eggs to get Tauros, Kangaskhan, Mr. Mime (16 incubator purchases).To have a 50% chance of getting the regionals (assuming you don't have Farfetch'd from a previous global event):If you're from NA (or AU): You need to hatch about 60 eggs to get Mr. Mime, Farfetch'd, and Kangaskhan (or Mr. Mime, Farfetch'd, and Tauros) (20 incubator purchases)If you're from EU: You need to hatch about 49 eggs to get Tauros, Farfetch'd and Kangaskhan (16 incubator purchases)Lastly, if you're from none of these regions (Africa, Latin/South America, Antarctica, Outer Space): You need to hatch about 64 eggs (21 incubator purchases).Happy hatching everyone! via /r/TheSilphRoad https://ift.tt/2OnILqd