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.
German legal experts with an average of more than fifteen years' professional experience were given a detailed description of a shoplifting case and asked to roll a pair of dice — secretly rigged to show either a 3 or a 9 — before recommending a prison sentence in months. Judges who rolled the higher number recommended significantly longer sentences on average than those who rolled the lower number, despite every judge knowing full well that the dice roll was random, irrelevant, and had nothing to do with the case in front of them.