The anchoring effect
Researchers have tested this many times, in different places, over many years, and they keep finding the same result. This one is safe to trust.
In 1974, two psychologists sat people in front of a wheel of fortune. What the people did not know was that the wheel was rigged to stop on only two numbers, 10 or 65. Each person watched it spin, saw it land, and then answered a question that had nothing to do with the wheel: what percentage of the countries in the United Nations are African? The people who saw the wheel stop on 10 guessed, on average, 25 percent. The people who saw 65 guessed 45 percent. Same question, same room, same afternoon. The only thing that differed was a number everyone knew was random, produced by a wheel, meaning nothing. It moved their answers by twenty points anyway.
The first number said in any conversation becomes the point everything else argues with, including in your own head. It does not matter that you know it is arbitrary. Knowing did not save the people watching the wheel. So the number you hear first in a price talk, a salary conversation, a negotiation, is quietly setting the range before you have said a word. The way to protect yourself is to write your own number down before the other one arrives.
Source: Tversky and Kahneman, 1974, Science. Re-tested on thirty six groups worldwide: Klein and colleagues, 2014.
Daniel Kahneman, 2011
The pull of numbers, explained by the man who measured it. Not a quick read, and it is not meant to be.
Draw your own card. It does not take long, and it rewards taking your time.