Anchoring is the tendency for an initial number — even one that's clearly arbitrary and irrelevant — to pull subsequent numerical estimates toward it. What makes anchoring especially unsettling is how little it depends on the anchor being remotely plausible or relevant, and how thoroughly it operates below conscious awareness: people reliably deny being influenced by an anchor even while their actual estimates shift measurably toward it.
This isn't a quirk limited to amateur guessers. Trained professionals making high-stakes judgments — judges, real-estate agents, appraisers — show the same anchoring effect, often while confidently insisting that an irrelevant number they were exposed to moments earlier played no role in their reasoning at all.