Balls into bins, with one choice and with two

Measure the gap between random assignment and the power of two choices.

1. assign_balls(n, d, seed) — throw $n$ balls into $n$ bins, each ball sampling $d$ bins uniformly with replacement and landing in the least loaded of them. Return the load array.
2. max_load(n, d, seed) and mean_max_load(n, d, reps, seed).

Then compare $d = 1$ against $d = 2, 3, 4$ as $n$ grows from $500$ to $20{,}000$ and check the two predicted shapes: $\log n/\log\log n$ against $\log\log n/\log d$.