I noticed for the first time today that if the average salary for their position is lower than what they are asking for, and you offer the average, you will win. I won 4 or 5 cases today doing this. For as long as I've played this game I would offer a a little less than their asking, maybe around 500k, and I don't win many that way. But offering the average seems to tilt things in your favor quite a bit.