Anchoring effects extend well beyond lab puzzles into real judgments people make about the physical and commercial world, and the anchor doesn't need to be plausible to work. Simply being asked to compare an unknown quantity to an obviously arbitrary reference number shifts a person's subsequent independent estimate toward that number — a fact well known to negotiators, real-estate agents, and marketers, who use it deliberately.
The defense against it is structural, not willpower-based: since the effect operates below conscious control, the only reliable countermeasure is generating an independent estimate before being exposed to any anchor at all, rather than trying to consciously discount an anchor after encountering it.