If you can save money with no out of pocket costs, than you have nothing to lose. If you want to gamble go to Las Vegas. It's a heck of a lot more fun Extra Tricks to Save Money When Refinancing The purpose of most refinance loans is simply to save money. The goal is to minimize your expense over the life of the loan or to minimize your monthly payment in the near future. If you can swing it, don't roll every cost of refinancing into your new loan.
Most people escrow for taxes and insurance.
If you do, your current lender must give you you escrow refund within 30 days of paying off their loan. Also remember that you always get to skip a month of payments. If you close June 5th, your first new payment is August 1st. On the other hand, some people love the fact that they didn't pay anything out of pocket to refinance, got a nice escrow refund check, then got to miss a mortgage payment. They use the 'extra' money to pay bills, go on vacation, etc.