Well the problem with this is that much of the time, the banks do not actually review offers within the first 5 days or so, giving them time to accumulate as many offers as possible, so they don't have to deal with low ball offers (which they simply do not respond to.)
Generally speaking there are three (yes 3) things that having the greatest impact on weather an offer is accepted.
1. Currency, both purchase price & earnest money
Offer what you think the property is legitatmetly worth, if you submitt "your best case scenario" generally speaking, the only response you'll get is seeing the house going pending, with someone elses offer. Have 2-3% earnest money shows you're serious also have your proof of funds to close.
2. Inspection period: If you know that you can get the inspection period down to 3 days, then make the inspection period as short as you can. Generally speaking you can get the inspection done with report in hand within 24 hrs. The bank sees this as your walking time, the longer the inspection period is the less likely you are to get an offer accepted.
3. Closing, the bank would love nothing more than to close in a week or two. If you're paying cash, this is all possible, due to the lack of needing all the back end loan work done. I would still suggest getting an appraisal as it will give you a lot of helpful information.
Time & Money, that's all the bank is interested in saving and making.
Sincerely your favorite Prudential agent, Jason Gomes