"Math: it takes an average of 473 eggs to breed a shiny through Masuda Method since Gen. VI."

TL;DR: log(1-0.5)/log(1-6/4096) = 472.842...I am trying to hunt for a shiny Rowlet through Masuda Method. Someone kindly offered me a female Lv. 1 Rowlet for a Lv. 1 Comfey. I searched for a Ditto and bred one for him from my Lv. 18 Comfey, and a trade was made. I was playing the game in English while this Rowlet speaks Spanish. Masuda Method activated.Hatching the eggs with my Lv. 70 male Decidueye generated boxes upon boxes of normal Rowlets. So how many Rowlets will this procesure generate before I have an average chance to find a Shiny? A good definition of "average chance" would be "over 50% probability," so I started punching a calculator using this metric.The events of "getting a shiny" and "not getting a shiny" are mutually exclusive, and upon hatching an egg either of the two will happen. Hence the sum of the probability of both events is 1. Through Masuda Method, the chance of getting a shiny is 6/4096. Hence the chance of not getting a shiny is 1-6/4096.Since I am talking about "getting at least one shiny" which can be fairly complicated to write a formala for directly, I am tackling the easier to calculate mutual exclusive of this event, "not getting any shiny." Each egg is independent of each other. The chance of not getting any shiny after n eggs would be (1-6/4096)n. With a 50% chance of getting a shiny, the chance of getting no shiny after all those egg would be 1-50%. Hence we get this formula representing "less than 50% chance not getting any shiny after n eggs", which is equivalent to "no less than 50% chance getting at least one shiny after n eggs:"(1-6/4096)n < 1-50%Solve for n by taking the logarithm of both ends of the equation, we get the formula listed above. Since it is impossible to get 0.842... eggs, we have to count it as a whole egg and the conclusion as the title is reached.Additional numbers:Without Masuda method, or during wild encounters, you will need 2839 eggs/encounters to have at least 50% chance to see a shiny. (damn you, CandyEvie, fund 2 shinies in one Let's Play)With Masuda Method, it takes 1571 eggs to have a 90% chance of hatching a shinyWith 2839 Masuda eggs, you have 98.44% chance of finding a shiny. via /r/pokemon http://ift.tt/2kWqu5f