How many bounded attempts one unit gets before the loop concedes. With per-try success p, k independent tries succeed with probability 1−(1−p)^k: at p=0.5, five tries ≈ 97%, and the sixth adds ~1.5%. So around five is "probably" — for independent tries.
The reason a cap exists at all: retries that see their own failure are not independent. The model doubles down on its mistake — re-making it, or flip-flopping between two wrong answers forever. That is a rogue loop, and it is an idiosyncratic property of these models, not bad luck. The stall detector (identical error signature, or a best-count that stops dropping) is the real stop; max passes is only the backstop ceiling. Raise it for weak free models — the stall detector prevents waste anyway; lower it to cap metered spend.