Gap Test
Every ball sits out sometimes — sometimes for one draw, sometimes for forty. Collect every gap between consecutive appearances for every ball, and the resulting distribution has a specific mathematical signature. Here's whether Powerball actually follows it.
| Gap (draws) | Observed | Expected | Bars |
|---|---|---|---|
| 1 | 473 | 480.1 | |
| 2 | 441 | 445.4 | |
| 3–4 | 867 | 796.2 | |
| 5–7 | 954 | 990.8 | |
| 8–11 | 1,000 | 1016.9 | |
| 12–16 | 940 | 908.0 | |
| 17–22 | 704 | 722.3 | |
| 23–30 | 558 | 572.6 | |
| 31–44 | 456 | 451.7 | |
| 45+ | 233 | 242.0 |
How it works
The setup. Every draw, five white balls are selected out of 69 — so any specific ball has probability p = 5/69 ≈ 7.25% of showing up. If draws are independent, the number of draws you wait between consecutive appearances of that ball should follow a geometric distribution with mean 1/p ≈ 13.8.
What we measure. For each of the 69 white balls, gather every gap (in draws) between consecutive appearances. Pool all 69 balls' gaps into one giant histogram, then compare against the geometric curve the math predicts.
The null hypothesis. If Powerball has hot-streak behavior (a number, once drawn, is more likely to be drawn again soon), gaps will pile up at the short end. If it has drought behavior (mean-reversion), gaps will pile up in the middle. If it's memoryless — the fair-lottery case — the observed bars should match the geometric curve and the chi-square p-value should be large (> 0.05).