Statistical Outlier?

Looking at the current stats (call them yourself in the GPT with prompt "stats") I found the distribution far from statistically plausible. At least so far, with 280 count total. Particularly odd is that 5-2 has not been drawn even once so far. I was curious how likely that is from a mere technical standpoint. So I asked GPT 4.1:

Is there anything in this php that could explain, why specifically within 280 hits 5-2 has not even been drawn once? It seems statistically unlikely. 

GPT 4.1:

Analysis of the code and statistical likelihood:

1. Randomness Source

• The outcome is determined by:

  $A = random_int(1, 6);
  $B = random_int(1, 6);
  

  • This uses PHP’s random_int, which is cryptographically secure (since PHP 7).

  • This function, if the system entropy is adequate, produces each value in the range [1, 6] with equal probability.

2. Possible Outcomes

• The "signifier" is always "A-B", where A and B are each independent, uniformly distributed random integers from 1 to 6.

• There are 36 possible combinations (6 * 6 = 36).

• For 280 trials, the expected count for each combination is:

  28036≈7.78\frac{280}{36} \approx 7.78

3. Statistical Likelihood

• Probability that a specific combination (e.g., "5-2") never occurs in 280 trials:

  • Probability that "5-2" does not occur in one trial: 35/3635/36

  • Probability that "5-2" does not occur in 280 independent trials:

    (3536)280≈0.000232\left( \frac{35}{36} \right)^{280} \approx 0.000232

  • This is about 0.0232% (about 1 in 4,300).

4. Code Examination for Exclusion of "5-2"

• There is no code that filters, manipulates, or avoids any specific combination.

• There is no manipulation of $A, $B, or $signifier that would suppress "5-2".

• The XML and JSON fetch/use does not feed back into the draw; it only handles the result.

• There are no conditionals or filters on $A, $B, or $signifier before storing or displaying.

5. Potential Non-Code Explanations

• Only non-code explanations remain:

  • Corruption or manipulation of stats.json: If stats.json was manually edited, reset, or not correctly written/read, that could lead to an inaccurate count.

  • Repeated process crashes or partial writes: If stats.json is not written every time, some outcomes could be underreported, but this would affect all outcomes randomly.

  • Concurrency or locking errors: Code uses file locks (flock), but in rare file system situations, race conditions could cause inconsistent stats. However, this is unlikely to selectively affect "5-2".

6. Summary Table

Conclusion:

• The code does not contain anything that would specifically exclude or bias against "5-2".

• The probability of not seeing "5-2" in 280 trials is approximately 0.023% (1 in 4,300), which is highly unlikely but not impossible.

• If the draw process is actually happening as coded, the most likely explanation is a statistical outlier.