First a history lesson: More than three decades ago, two psychologists conducted an experiment that was equal parts funny and deadly serious.

They spun a roulette wheel and when it landed on the number 10 they asked some people whether the number of African countries was greater or less than 10 percent of the United Nations. Most people guessed that estimate was too low. Maybe the right answer was 25 percent, they guessed.

The psychologists spun their roulette wheel a second time and when it landed on the number 65, they asked a second group whether African countries made up 65 percent of the United Nations. That figure was too high, everyone agreed. Maybe the correct answer was 45 percent.

The difference in the estimates of the two groups was tied to the original number they were given. It made no difference that the number was meaningless: It came from a roulette wheel. Psychologists Amos Tversky and Daniel Kahneman described the error as caused by a phenomenon known as anchoring -- when you don't know the answer to something, whatever starting point you have plays a powerful role in determining what you think is the right answer.

Flash forward 32 years. A Johns Hopkins study published in a respected peer-reviewed journal finds the number of Iraqis killed as a consequence of the 2003 invasion to be about 650,000. Critics immediately get up in arms; President Bush -- not known to be a keen evaluator of scientific studies -- declares the result "not credible."

Although the debate over the study has been largely driven by the political implications of the number of Iraqi casualties, psychologists say the fact that many people find the new number hard to digest is a perfect example of anchoring.

Previous estimates had put the number of Iraqi casualties at 30,000 to 50,000. Once that number was anchored in people's minds, it was a foregone conclusion that most people would find it very difficult to accept a much larger number.

"It could be malicious and deliberate or innocent and just wrong, but the fact that the administration had set an anchor is what makes the new number seem implausible," said Max Bazerman, who studies human decision-making at Harvard Business School.

It is important to remember that the psychological phenomenon does not tell you what the correct number of casualties in Iraq really is. But it does say that even if the 650,000 number is accurate, we are likely not to believe it.

Like many other aspects of human behavior, psychologists say anchoring is just one way the brain makes sense of the world. We assume the information we are given is at least somewhat accurate, and therefore use that as an anchor around which to evaluate new information or make informed guesses. Like other subtle biases, anchors influence people at an unconscious level. Neither group in the roulette-wheel experiment realized it had been subtly manipulated.

Anchoring effects have been observed in a wide array of activities. Wesleyan University psychologist Scott Plous has noted that the phenomenon has been noted in getting estimates about "the percentage of working mothers with children under the age of five, the proportion of Iranians who are Islamic, the percentage of chemistry professors who are women." In a book he wrote about how human beings make decisions, Plous noted that politicians and others who seek to influence people "will generally be most successful by staking out extreme initial positions."

Although anchoring is often innocuous, it can sometimes come at a cost. Psychologist Nicholas Epley at the University of Chicago said that people who move from a city with expensive housing to one with cheaper housing are likely to overpay for housing because their minds are still anchored in the more expensive market. The length of a sentence that prosecutors demand influences what kind of punishment judges and jurors impose for identical crimes.

One study by psychologists Greg Northcraft and Margaret Neale showed that real estate agents given a lower starting price for the cost of a home concluded the house was worth less than those given a higher starting point.

Epley said he conducted one experiment in which asking people how much money they had in their wallets vs. how much they had in their bank accounts influenced how much they spent. When the experiment was conducted outside a store before shoppers went in, those who were reminded of the larger amount that was in their bank balances spent more than those who were reminded about the smaller amount in their wallets.

Is there a way to avoid the anchoring bias? In situations such as the Iraq war, in which there is genuine uncertainty about what has happened, there is not much that people can do apart from being aware of the anchoring bias and eyeing everything with healthy skepticism. But in some situations, Epley said, there is indeed a way around the anchoring bias.

"In what year was George Washington elected president?" he asked. "You don't know. But you know Independence was declared in 1776. You know it is later than that. Is it 1778? 1780? The anchor is in the ballpark. It gets you closer than just pulling the answer out of a hat."

What's the only way to avoid the anchoring bias altogether? Know the right answer. George Washington was elected president in 1788.