Every ball on the Galton board makes the same simple decision at each peg: bounce left or right, with a coin-flip's worth of randomness. No ball "knows" about a bell curve, and no two runs ever drop in exactly the same pattern — the shape only emerges once you add up thousands of independent random choices. That's the Central Limit Theorem in physical form, and it's exactly the same mathematics behind why so many unrelated things in nature — heights, measurement errors, exam scores — end up roughly normally distributed.
An IQ score of 130, with a population mean of 100 and standard deviation of 15, has a z-score of exactly 2.0 — and by the 68-95-99.7 rule, only about 2.3% of people score that high or higher.
Each ball's path depends on genuine random numbers generated fresh every time you press play — there's no fixed script or seed behind it. Run it ten times and you'll get ten different exact patterns, even though the overall bell-curve shape stays remarkably consistent — that consistency-despite-randomness is the entire point.
It shifts the probability of bouncing right at every single peg away from 50/50 — push it toward 0.9 and the whole distribution skews hard right, since each ball is now far more likely to drift that way at every one of its many decisions.
Each row adds one more independent random decision. More decisions per ball means more possible final bins and a distribution that sits closer to the smooth, continuous normal curve — the discrete binomial distribution converges to it as the row count grows.
Use the population formula (divide by n) when your data is the entire group you care about; use the sample formula (divide by n−1) when your data is a smaller sample standing in for a larger population — dividing by the slightly smaller number corrects for the fact that a sample tends to understate the true spread.