Editing Openai/69434f20-ed90-800d-ab60-60312c9de3dd (section)

=== Assistant: Assessment of Captain Blue’s reply content & validity: ===
Assessment of Captain Blue’s reply (content & validity):

On the math/statistics
* Captain Blue’s AI-derived answer is mathematically conditional, not “concrete.”
* The AI result is correct only under explicit assumptions: - Random distribution of cheaters. - Full 20-player exposure (or near-full) per match. - Independence between matches.
* Captain Blue partially concedes this by adding: “If your game uses smaller effective opponent pools, adjust the exponent…” — which undercuts his earlier claim of concreteness.
* Therefore, Loctarjay’s critique still stands: the statistic is scenario-dependent, not universally applicable.

On the “fabrication” accusation
* Captain Blue is correct that Loctarjay’s proposed table would answer a different question.
* However, Loctarjay’s point was not that Captain Blue fabricated numbers, but that: - AI outputs are highly sensitive to framing, and - Captain Blue presents a conditional probability as a definitive real-world claim.
* Showing a screenshot does not resolve the assumption problem.

On credibility & argument strength
* Captain Blue relies on AI authority + screenshots, but does not defend the realism of the assumptions.
* Loctarjay focuses on model validity and hidden premises, which is the stronger epistemic position.
* Captain Blue’s repeated framing of the result as “concrete” remains inaccurate.

Bottom line
* Captain Blue’s math is internally correct but externally overstated.
* Loctarjay’s criticism addresses how the math is being used, not whether AI can calculate probabilities.
* The dispute is no longer about math ability — it’s about misrepresenting conditional probabilities as proof of real-world cheating frequency.