Simulation & Resampling

Some questions are easier to answer by simulating them directly than by deriving a formula: how much would a statistic vary if you resampled your data, how extreme is an observed difference under random relabeling, or how likely is an event under a transparent random model. Every engine here uses a seeded, fully reproducible pseudorandom generator, never an unseeded source, so results can always be exactly reproduced from the reported seed.

None of these tools are cryptographically secure, and none claim to be; they exist for statistical exploration, teaching, and planning, not for security-sensitive randomness.