here's the "experiment" being conducted here: - start with an urn with, say, 3 green balls and 3 red balls (controlled via "successes" and "failures" sliders respectively) - until the urn has 100 balls, repeatedly draw balls from the urn; each time a ball is drawn, add it back to the urn along with a copy of the same color - count the number of green balls at the end - do that like ten thousand times and see the distribution of the results there's actually a very fancy distribution that can model these precisely and account for all the skew and whatnot but it sounded kind of confusing so instead of learning about that i just made a funny little tool for looking at the distributions. the line drawn after the simulation shows the closest normal distribution -- tends to fit better if the urn starts with a few of both types of ball, with more even amounts leading to more normal distributions. the graph in the top right corner shows how well the normal distribution fits the actual data by comparing the actual z-score of each data point to the expected z-score based on percentile. (distance between axis ticks is 1 standard deviation)
