The more I thought about this the more I'm not sure what I was talking about, so just ignore math attempts in the previous post and look at the pretty pictures in this one.
Your decison tree to get the guy could look like this:
And hers like this:
If it is guy 1 or 3, she will never win, but she is doing well.
If you use a better tree:
You'll do better. She'll still get those quick wins in that kill your spirit, but you'll grind out victory.