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.
Kahneman and Tversky rigged a spinning wheel to stop only at 10 or 65, then asked participants to estimate the percentage of African nations in the United Nations right after seeing which number the wheel landed on. Despite the wheel obviously being random and irrelevant to the question, participants whose wheel stopped at 65 gave much higher average estimates than those whose wheel stopped at 10. In a separate, much higher-stakes version of the same effect, real-estate agents were shown an actual house for sale along with a full information packet, but given either a substantially higher or lower artificial 'listing price' than the real one — and their professional valuations were significantly swayed by this anchor, even though most agents denied afterward that the listed price had influenced their judgment at all.