A fixed audit of the official draw record
The Hottest Ball Is Still Cold
Ball 61 appeared 125 times while ball 13 appeared only 76 times in the first 1,398 drawings of Powerball's current 5-from-69 format. That gap looks like a system until the page repeats a published lottery test with the official draw file: the correctly calibrated single-ball p-value is about 0.0877, and the much deeper pair test gives about 0.543. The conspicuous hot and cold balls are not evidence of a usable edge in this fixed audit.
LOCKED WINDOW2015-10-07 to 2026-08-24white balls only1,398 draws
Layer 1 · the conspicuous ball
Put your finger on the outlier
Click 61. Every red tick is a draw where it appeared, and every date is in the ledger. Then run the whole 69-ball audit. A hot ball does not get judged alone after it has won our attention.
Choose one ball for its dated ledger. Choose a second to switch the ledger to a pair.
Choose a ball to light its dated occurrences.
Not rejected at α = 0.05. Raw X² = .... Sampling five balls without replacement shrinks the ordinary Pearson variation by 64/68, so the correct comparison uses X²/(64/68) against chi-square with 68 degrees of freedom.
This is a failure to reject equal marginal frequencies in this window. It is not proof of a fair machine, and it is not a forecast.
Layer 2 · the frequency-preserving objection
What if every ball is ordinary, but the company it keeps is not?
A marginal audit can miss a mechanism that preserves all 69 individual counts while distorting pairs. The subset test of Genest, Lockhart and Stephens asks all 2,346 unordered pairs at once. Open the full matrix, touch any cell, and inspect the dated pair ledger before running its weighted null law.
3 + 16 occurred 15 times; null expectation 5.9590793.
Brighter cells occurred more often. The diagonal is undefined because no white ball can repeat within a draw. The selected cell has a gold outline.
The recorded seeded calibration is shown above. Press run to recompute it live from 3.8208955224 × chi-square₆₈ + 0.9118046133 × chi-square₂₂₇₇ using seed 0x61c0ffee.
The global pair audit remains ordinary. Pair 3 + 16 is the hottest observed cell at 15, against expectation 5.9590793, but it was selected only after all 2,346 cells were seen. It does not receive a private p-value.
The check · an instrument with teeth
Free choices: cutoff 2026-08-24, current 5-from-69 era only, white balls only, c = 1 and c = 2 subset tests, α = 0.05, seed 0x61c0ffee, and 10,000,000 Monte Carlo samples.
Uncertainty: the weighted laws are asymptotic. The pair p-value is seeded Monte Carlo, not an exact tail integral; its standard error is about 0.00016. Equal marginals and pairs do not establish serial independence, higher-order uniformity, machine integrity, or future outcomes. Hot and cold labels are retrospective.
Why the ordinary Pearson table is wrong here
Five white balls are sampled without replacement. One ball appearing in a draw makes another slightly less likely to appear in that same draw, so the 69 counts do not vary as independent categories. For single balls, the raw Pearson statistic is scaled by (69 - 5)/(69 - 1) = 64/68. For pairs, the null is the weighted sum 3.8208955224 × chi-square₆₈ + 0.9118046133 × chi-square₂₂₇₇. Those are the lottery-specific calibrations, not decorations added after seeing the result.