The staring contests that I often play are much better than a simple "do not turn away" or "do not blink". Mine have three simple rules:
1. Do not laugh.
2. Do not touch the other person.
3. Do not break eye contact.
It's much more fun, now that you need to be creative, trying to get the other person to play. You're in for trouble if you get a beautiful seductive lady (or handsome seductive man, though I wouldn't know if that matters) playing against you, but be strong. If you're just starting out, you're screwed, as newbies never win (unless you are a beautiful seductive lady). Games of this fashion can last hours at a time. I have spent five continuous hours on some games, only to have to stop them and resume the next day because the sun has started to come up.
The tactics that people use are as varied as the smells of different cheeses. Some, however, that I suggest, are: be a seductive lady, pretend to be a seductive lady if you are a man, explain faith healing, make an ass out of yourself, hit on ugly people. Good luck.