There are many variables that go into what to bid on a home. The first thing to determine is what is Fair Market Value(FMV) of that home. Fair Market Value is determined by finding at least 3 similar properties that have sold in the past 6 months. That number is what a group of buyers would be willing to pay for the property today.
FMV should also take in to account the condition the property is currently in. Anybody can list a home for any price.... including banks. The questions is what would a pool of buyers be willing to pay.
Whats you determine fair market value the question is what will a bank accept. It all depends. 50 cents on the dollar of a home price well would be a pipe dream. Most bank want pretty close to what the home is listed for. Many times you will see an REO home drop in price multiple times before selling, meanwhile rejecting decent offers alont the way, many times selling for less than a higher offer they had in the past. This is just the way the banks work.
As an agent, I would encourage you to put in an offer no matter what it is, but you will quickly learn your spinning your wheels until you start to understand the Fair Market Value of a property. And, yes it is possible to get a bank own home under FMV but it all depends on the circumstances.