What's your best offer?

OH NO! This is going to get tricky!!! I just heard back from the other Realtor about the house we made an offer on.........to say the least.....this is going to be tough! Our offer was turned in with another offer from ANOTHER investor.....Apparently, he had a low ball offer too. The bank has countered back (it's a foreclosure) to both of us with....... "make your best offer and we will take the highest one". What the hell!?! I mean that sounds easy right? I swear it's not! There is so much to think about on a real estate contract it's not even funny! I mean first of all, the house is a dump and I don't think I want to make my BEST offer EVER on a peice of crap on a slab like that haha. Anyway, what is a good offer? If we offer X amount of dollars and ask them to treat for termites and the other people offer X amount of lower dollars and DONT ask to treat for temites...then they might win with a lower dollar offer. Then, there is also another real estate trick......alot of people will assume that the other bidder will offer like $50,000 even....so the other bidder will offer $50,000.01 so they could win by a penny. Now, that is common knowledge......so do we offer X amount plus 3 dollars? I generally don't mind this kind of thing...it's a game to me. However, Chase, is a different story........he will HATE doing this. He hates to sit and think....."What if I offer too high and I paid over what I had to.....or what if I offer too low and I miss out by a few dollars." It's just a one shot chance....there are no counters.....highest offer wins! So who is this fellow we are going against? I wish I knew so I could investigate. Is he a veteran real estate investor or just a good ol boy tryin to buy a house? Hmm....we'll see. I haven't talked to Chase about the deal yet, but it will be interesting to see what Chase offers. He will throw an odd ball number!