As your tagline is "low ball offers get the prize" it appears that making low ball offers is your standard operating procedure. Realize that an unreasonable offer (way below market value) may simply get you a rejection and no second chance.
Deborah is also correct you'll never know what a Seller is willing to accept unless you make an offer.
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Along the same lines as the previous answer, it's likely that the house was substantially overpriced when it came on the market. Example: The house really is worth $195,000. It came on the market at $230,000 and has had a price reduction of $5,000 every two weeks. It's now priced at $215,000. It's still overpriced. You make what you think is a low-ball offer at $200,000. It's accepted. You think you got a real bargain. Actually, you've overpaid. And it might not appraise for that much.
So it's very important that you know what the house really is worth before making the offer. Then offer something equal to or lower than its real value.
Whether the sellers will consider any offer is impossible to say. It really depends on their degree of motivation. But the only way to know for sure is to make the offer. If it's countered, that's an excellent sign. If it's accepted, ironically, you might have overpaid.
Ask your Realtor for more information.
Hope that helps.