Random selection is widely used in resource allocation and auditing, making reliable implementation essential for AI-agent systems. Behavioural tests across six reasoning models uncovered threshold and divisibility rules used in identifier-based choices. For threshold-following GPT-6 Sol and Gemini 3.8 Flash, single-agent measurements prospectively predicted correlated participation under shared identifiers and biased participation under distinct identifiers with common timestamp bits. Changing dates, formats and identifier labels revealed when these predictions held. Explicit instructions to randomize independently reduced but did not eliminate shared-input correlation. To test implications for oversight, we asked four models to select customer requests randomly for human review. GPT-6 Sol approached the target rate while selecting predictably from identifiers; the others rarely selected requests. All four closely followed supplied random draws. These findings expose collective and audit vulnerabilities that selection rates alone miss, making input-dependent bias, correlation and predictability central targets for agent evaluation.

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