Most people really do not know how to buy a home and realtors know that. Remember Information is like gold.
What we have done when we liked a home to buy is thoroughly research the owners (and the home). All info is public record and in Florida it is all on line and free.
Important factors are, what is the owners mortgage, any other liens or encumbrances on the property, or is it owned outright.
If they are mortgaged fully, they are less likely to accept a low offer less than their leveraged amount.
If they own it outright, that is another opportunity to offer less as the seller is not gong to be out of pocket. (Remember we NEVER count home equity in our retirement nest egg)
If they are leveraged and the amount is 30% - 40% less than the perceived value of the home you can offer as low as the mortgage + RE fees and it will be considered.
Case in point, In 2006 a home was listed in a nice development in Florida for $1.2m, that was at the height of market. It came off the market and the owners rented it for 2 years, in 2008 it went back up for $870k. The buyers researched the owners, they had a $575k mortgage on the home and another home in California that was also mortgaged for $650k.
The original home was listed for 2 months and reduced to $740k. A buyer placed a cash offer with some contingencies for $500k, it was rejected. After 1 week, the same buyer place a cash offer of $595k No Contingencies (other than home inspection) and stated it was the last offer from this buyer and would expire permanently in 48 hours. 1 hour prior to the expiry it was accepted.