📖 The Science: Why Humans Cannot Generate True Entropy
1. The Gambler's Fallacy (Alternation Bias)
Humans switch between digits far too frequently (often ~65% of the time in binary, instead of the 50% theoretical expectation). We intuitively feel that after a '1', a '0' is "overdue".
2. Streak / Run Starvation
In a true random binary sequence of 60 bits, there is a >90% chance of a streak of 4 or more identical symbols ($E[\max L] \approx \log_2 N$). Humans actively avoid long streaks, starving the sequence of natural clusters.
3. Sequential Martingales (Solving Peeking)
Evaluating randomness after every key with standard p-values causes false-positive explosion. This app implements Test Martingales and Ville's Inequality, guaranteeing that false rejections are strictly bounded by $\alpha$ over indefinitely long typing.
4. Universal Online Predictor
An adaptive multi-order Markov mixture (PPM / Context Tree) learns your personal typing grammar in real-time. If it can guess your next key with >50% accuracy (or >10% in decimal), your sequence is compressed and non-random.