Disliked{quote} This is of course true as all flips are independent of each other, but why does a large number of flips follow a normal distribution? I have trouble reconciling the two ideas in my mind.Ignored
what about a 20 sided die? after landing on 1 49 times, what is the next number going to be according to probabilities?
but what do i know. someone who loves playing with excel can surely toss-up a formula to count how many times you get 49 heads plus one more head versus 49 heads plus a tail.
i think when you are looking at your normal distribution you are only really seeing half of an answer to the wrong question. my fingers and toes maths suggests to me the chance of getting 49 heads and a head is the same as 49 heads and a tail, just as you are just as likely to get 49 heads or 49 tails. when you look at the distribution you focus on the run, not on the SPECIFIC PATTERN ITSELF out of all possible combinations for that number of flips. EDIT: <-- I'm saying this is probably what you are doing, and incorrectly. you are distracted by one thing and reading it as being another.
it's a game of plinko, but you are stuck looking at the second last rung, not the last rung.
or another way to look at it is, again as a game of plinko, is that the results in the middle have the most common column ancestors and were inbred, whereas the results towards the edges had less common ancestors and literally branched-out. they were less likely (i.e. it was impossible) for them to return to the common pool towards the middle by the time you cut them off at some number of iterations. what you are measuring is the likelihood of inbreeding, so to speak.
or another way to look at it is "because fuck you, that's why". don't fight it. embrace the dark side.