"Probability Reminder: Odds of a shiny after N encounters"

#PokemonGO: Since there have been many posts recently discussing terrible luck with finding a particular glimmering hat-wearing rodent, I thought it might be a good time for a little reminder on calculating the probability of an event occuring after several attempts.(1-(Probability Of Thing You Want With One Try))Number of Events=(1-(Probability of Getting What You Want))Don't forget the "1-" parts!So, if we assume the probability of seeing a shiny is 1/250, and someone has checked 500 Pikachus: (1-(1/250))500 =0.1348Which means there is a 13.48% chance of NOT finding a shiny in 500. And that's... not really terrible odds honestly. To provide a second example (and to make those without a shiny hat-chu feel a little better), I wasn't able to get outside during the Dratini event and ended up with only 30 dratini spawns through incense and a lure. What were my odds here assuming a purple dragon is a 1/25 occurance?(1-(1/25))30 =0.2939So although I had a 70.61% chance of getting one, I came out empty handed. And don't forget that this equation applies to many other things, such as odds of catching a raid boss after N ball throws!For slightly more advanced mathers: We can also use logarithms to go the other way to find how many events are needed for a certain percentage chance at success. This is:log(1-(Probability of Success Overall))/log(1-Probability of Single Event)= Number of Events NeededSo to be 99% sure to get a shiny Pikachu (assuming the 1/250 odds), we would need at least 1149 encounters! (my condolences to those of you in the 1% here) via /r/TheSilphRoad http://ift.tt/2FdSI8s