Just in case you don't know. I can't quite tell by your post. Points only come into play as a 1st choice. It doesn't matter if you have 20 points going into a 2nd choice. They won't matter. 2nd choices are a random pick. As are 3rd and 4th choices. It's all luck.
You have two choices if you want to hunt with good odds for a 2nd choice. Take a cow as a 2nd choice, or hunt a bull in an OTC unit. Actually, the OTC is a sure thing, and the cow is close if you pick the right unit.