I have had buyers who have their first offer accepted, and others that have written ten offers. If your Realtor has a good local reputation, and the respect of her peers, your odds of an accepted offer will increase. However,
there are other factors, such as: 1. How many homes are on the market and how many buyers are looking?
2. Downpayment. Typically a buyer with a larger down payment will have an edge over a buyer with a lower down payment, such as FHA 3.5% down. 3. Buyers looking for homes that are in "move-in" condition will have more competiton. 4. Homes under $350,000 are more in demand, with more competition.
It is important to have a pre-approval letter from a direct lender, proof of your funds for a downpayment, and a clear strong offer. I always write a cover letter for my clients, which can often help. The key is to NOT give up and be sure you have chosen a Realtor who will keep you updated immediately on new listings. Be as available as possible to come out and look at the home.