"Mathematics on probability of seeing a Halloween shiny"

#PokemonGO: The odds of a shiny Halloween have been stated to be around 1 out of 256 (correct me if I'm wrong … but even if I am, this still is good math info).Saw a post/question where someone said “the odds couldn't be 1:256 since he had caught 300 and still hadn't seen one”. It might not be obvious but that’s not how probability works, and so I thought it would interesting to show how probability does work for stuff like this.Let’s start with a typical die. It has 6 sides. The odds on getting any single value (a 4 for example) on a single roll is 1 in 6. However, much to the point of the person’s statement above, that does not mean that after 6 rolls, you are guaranteed to get a 4. It’s a good possibility, but what are the true numbers? What is the possibility of getting a 4 somewhere within 6 rolls? Here’s how you do it (and we’ll relate this back to shiny Pokemon in a sec).Instead of looking at the odds of getting a FOUR on roll one, and then if not, roll again (and calculate it several more times, it’s easier (math-wise) to look at the inverse: what are the odds of NOT getting a FOUR for six consecutive rolls?The odds on NOT getting a FOUR is 5 out of 6 (about .83, or 83%). To calculate that happening 6 times in a row, it’s .83 times itself for 6 times… or .83 x .83 x .83 x .83 x .83 x .83 … this is also .83 to the 6th power, or (.83)6. This calcs to about .33 (or 33%). If we didn’t see a FOUR 33% of the time, then we did see a FOUR in the roll somewhere along the line in all those other possibilities, which is 67% (100% - 33% = 67%). So, if you roll a die 6 times, you’ll get a FOUR somewhere in those 6 rolls about 67% of the time.Now, back to Pokemon. If we assume the odds of a Shiny are 1/256 (which is a measly 0.4%), the odds of not getting a shiny are 255/256 (or .996). Using the same math as above…The odds of not getting a shiny for two pokes is .996 x .996, or .9962, which is .992 (still over 99%)The odds of not getting a shiny for ten pokes is .99610 = .96, or 96%The odds of not getting a shiny for fifty pokes is .99650 = .82, or 82%The odds of not getting a shiny for 100 pokes is .996100 = .67, or 67%The odds of not getting a shiny for 300 pokes is .996300 = .30, or 30% (etc)So, after seeing 300 halloween pokes, you still only have a 70% chance of being lucky enough to have seen one somewhere in those 300. Or, to look at this another way, if 100 people all saw 300 halloween pokemon, 70 people would have seen at least 1 shiny, but 30 people would not have seen even a single shiny. :(Hope that all makes some sense … interested to hear the replies. via /r/TheSilphRoad http://ift.tt/2z8cuPs