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Randomness Proof

Verified Random1,332 draws · Oct 7, 2015Apr 4, 2026

We subjected 1,332 Powerball red ball draws — every draw since the pool was reduced to 26 on Oct 7, 2015 — to the same battery of tests used to break ciphers and identify random number generators. The result: statistically indistinguishable from true random.

Draws Analyzed
1,332
Since format change (Oct 7, 2015)
Index of Coincidence
0.0384
Random = 0.0385 | English = 0.0667
Chi² vs Uniform
p=0.487
χ² = 24.57 (25 df)
Classification
CSPRNG
Moderate confidence

3D Spectral Test

Every three consecutive draws form a triplet (Yn, Yn+1, Yn+2) plotted as a point in 3D space. If the draws came from a pseudorandom generator, the points would cluster onto parallel planes. Our data fills the cube uniformly — no lattice structure.

NIST SP 800-22 (Bit-Level)

1/9 passed — expected, due to 5-bit encoding of values 1–26

Frequency (Monobit)FAIL
RunsFAIL
Longest Run of OnesPASS
DFT (Spectral)FAIL
Serial (m=3)FAIL
Serial (m=5)FAIL
Approx. Entropy (m=3)FAIL
Approx. Entropy (m=5)FAIL
Cumulative SumsFAIL

NIST tests operate on bits. Values 27–31 never appear in 5-bit encoding, creating structural imbalance unrelated to source randomness.

Value-Level Tests

4/4 passed — integer-level tests bypass encoding artifacts

Linear Complexity
L = 1,000 (1.00× expected)PASS
Maurer's Universal
f(n) = 5.140PASS
Gap Test
mean = 25.45PASS
Runs Up/Down
925 runsPASS
1/9 bit-level vs 4/4 value-level
The source is random. The encoding isn't.
Chi² vs uniform24.57 (p=0.487)
Index of Coincidence0.0384 (random = 0.0385)
Entropy ratio0.997 (4.687 / 4.700 bits)
Flatness ratio0.816 (1.0 = perfect)

PRNG Identification: 35 Generators Tested

We brute-forced 35 pseudorandom number generators across 10,000 seeds each, searching 100,000 stream positions per seed — roughly 35 billion comparisons.

Mersenne Twister
4 output mappings
9 partial (max 7/1,337)
LCG Family
8 generators × 2 mappings
Dozens of 6-value matches
XorShift32
12 shift triples
Scattered 6–7 value hits
XorShift64
1 generator
2 partial matches
SplitMix64
1 generator
0 hits
PCG32
1 generator
4 partial (6/1,337)
NO FULL MATCH FOUND
Best result: 7 consecutive values out of 1,337. With a 6-value signature from alphabet of 26, the false-positive rate is (1/26)6 ≈ 1 in 309 million — exactly what we observed.

Source Classification

Two independent classifiers converged: the cryptographic fingerprinter and the statistical analysis suite both scored CSPRNG and true random as the top hypotheses.

CSPRNG (os.urandom / secrets)
5
True random / hardware RNG
4
Stream cipher (ChaCha/Salsa)
2
Unknown structured source
2
Block cipher CTR (AES/DES)
0
Hash chain
0
RC4
-2

Anomalous Transitions

With 676 possible transitions and a z > 3 threshold, 1–2 false positives are expected by chance. We found 3. This is noise, not signal.

E→R
Observed: 8 · Expected: 2.2
z-score: +3.86
Z→D
Observed: 7 · Expected: 2
z-score: +3.60
N→R
Observed: 7 · Expected: 2.3
z-score: +3.04

What This Means

Equal Probability

Every combination has the same chance of being drawn. There is no exploitable structure in the draw sequence.

Historical Patterns Are Noise

The 3 anomalous transitions and lag-2 autocorrelation will not persist in future draws.

Combinatorics Is All That's Left

The only real differences between tickets are structural — parity, spacing, range coverage.

Read the Full Technical Analysis →

Every Powerball drawing is an independent random event. No system can predict or influence the outcome. Balliqa identifies structurally balanced picks based on combinatorial probability, but this does not increase the probability of winning.

DISCLAIMER: Balliqa is an entertainment product. Every Powerball drawing is an independent random event. Pattern analysis of historical draws does not predict or influence future outcomes. The odds of winning the Powerball jackpot are 1 in 292,201,338.

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