Testing a 19 outcome RNG for an anti repeat filter and lag structure
November 10th, 2026 at 6:55:27 PM
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I have a long public series of categorical draws with 19 symbols (coded 0-18). Draws occur about every five minutes, from an electronic roulette-style lottery RNG. I am looking for statistical tests, not a betting system.
What the history shows:
- In a daytime window (roughly 07:38-19:59 local time), the same number almost never comes out on the very next draw (empirical repeat rate ~0%). Under independent uniform draws the repeat rate should be about 1/19 = 5.3%.
- Late at night the repeat rate is about 5%, close to that baseline.
- There looks like additional dependence at lags 3 through 8, beyond the lag-1 effect.
- Symbol "0" appears about 10% less often than 1/19, across the day.
- I already checked several daily-seeded 32-bit generators (MSVC/ANSI rand, glibc rand, Java LCG, .NET LCG, MT19937) against the series and did not get a credible match.
I would like to tell two stories apart:
A. Draws are close to uniform, but during the day the engine rejects (or resamples) when the new draw equals the previous one.
B. A single biased or Markovian generator whose transition law just happens to look different by time of day.
Questions for this board:
1. What tests would you use to separate (A) from (B)? Nested models / likelihood ratios, a pair of 19x19 transition tables, something else?
2. Under a pure lag-1 reject-and-resample rule, which lag-2 and lag-3-8 signatures should I still expect (for example P(X_t = X_{t-2}) = 1/18 rather than 1/19), and how do I test whether lags 3-8 contain extra structure after that is accounted for?
3. How would you distinguish a lag-1 anti-repeat filter from a shuffled-bag / without-replacement generator (coupon-collector counts in windows of length 19, etc.)?
4. If the day/night split might instead be two operators rather than a clock, what is a clean way to test whether the window edges stay pinned to the same minute on weekends and holidays?
I can share anonymized contingency tables (repeat counts, 19x19 transitions by period) if that helps keep answers concrete.
Disclosure: I drafted this question with help from an AI assistant; the data and questions are mine.
What the history shows:
- In a daytime window (roughly 07:38-19:59 local time), the same number almost never comes out on the very next draw (empirical repeat rate ~0%). Under independent uniform draws the repeat rate should be about 1/19 = 5.3%.
- Late at night the repeat rate is about 5%, close to that baseline.
- There looks like additional dependence at lags 3 through 8, beyond the lag-1 effect.
- Symbol "0" appears about 10% less often than 1/19, across the day.
- I already checked several daily-seeded 32-bit generators (MSVC/ANSI rand, glibc rand, Java LCG, .NET LCG, MT19937) against the series and did not get a credible match.
I would like to tell two stories apart:
A. Draws are close to uniform, but during the day the engine rejects (or resamples) when the new draw equals the previous one.
B. A single biased or Markovian generator whose transition law just happens to look different by time of day.
Questions for this board:
1. What tests would you use to separate (A) from (B)? Nested models / likelihood ratios, a pair of 19x19 transition tables, something else?
2. Under a pure lag-1 reject-and-resample rule, which lag-2 and lag-3-8 signatures should I still expect (for example P(X_t = X_{t-2}) = 1/18 rather than 1/19), and how do I test whether lags 3-8 contain extra structure after that is accounted for?
3. How would you distinguish a lag-1 anti-repeat filter from a shuffled-bag / without-replacement generator (coupon-collector counts in windows of length 19, etc.)?
4. If the day/night split might instead be two operators rather than a clock, what is a clean way to test whether the window edges stay pinned to the same minute on weekends and holidays?
I can share anonymized contingency tables (repeat counts, 19x19 transitions by period) if that helps keep answers concrete.
Disclosure: I drafted this question with help from an AI assistant; the data and questions are mine.
