Depends on what property the draw is at, compared to what your private ground is like.  I usually put in for the draw as a backup, selecting the later dates.  I have such good luck on the properties I hunt that I usually don't go if I get drawn.  Certainly not going to waste opening day or two on a draw.  But if I strike out in my hotspots then I'll go.  If I didn't have property with good bird populations to hunt it would be different.  I would check with the DNR on past harvests at the draw properties your considering.