There is an array of numbers to consider. The asking price carries very little importance except how many buyers will be attracted to the property. There is market value, which is difficult to estimate in a strong sellers' market. There is the price that your buyer can pay based on their financial situation, and there is the price that they would like to pay.
Since they can't pay more than they can afford, their offering price will fall somewhere between the last two numbers. Several factors will influence their decision: How badly do they want the property, what's their BATNA - do they need a home, and do they believe the values will continue to rise? Only the buyer can answer these questions; the agent helps them build the framework. It's your job to help your buyer establish a reserve price, which is defined as the price at which they are indifferent between a deal and no deal.
"The price at which I am indifferent
between a deal and no deal."
If they want the property, and there are several other offers, your buyer will likely choose to offer their reserve price. Holding anything back creates a risk of losing the property and isn't prudent unless the buyer is ok with that risk.
(Courtesy of The Nature of Real Estate)