Only way I can tell is to have a friend duel you and then they can tell you. But, I have only had one friend duel...so that may never happen. Would be nice though. It would also help to know what the pick up card actually is...is the first in the deck? Because it is not the strongest card, and it seems to not even be the rarest card like many have suggest.
No, it doesn't work like that. On the details page, it says it "You can earn more points by dueling opponents who have accumulated a large amount of event points". The win-rate doesn't matter.