I heard this phrase that sounds like 「いいえ、一手のさで、私どもの勝ちです。」, which in the context should mean one is one step behind, or one move too late, or being overtaken by someone else in doing something. But I cannot catch what the last part (after の）means. I don't actually know for sure if the first two is 一手, but it looks to me the only possible fit. After の it might have been さて instead of さで, but I cannot search online with just this.
I am fairly sure this is not slang/colloquial, so I doubt it's a modification that does not appear in dictionary. What is the exact phrase, and if I heard wrongly what is the closest to this?