Central Limit Theorem: Each ball makes n independent binary choices (left/right with probability p). The sum of n i.i.d. Bernoulli(p) variables has mean np and variance np(1−p). The CLT guarantees the distribution approaches N(np, np(1−p)) as n→∞. With 12 rows, already indistinguishable from Gaussian. The fitted Gaussian curve (white) is overlaid on the histogram. Bias p≠0.5 shifts the peak; the shape remains Gaussian.