Topics for doctoral candidates in mathematics

I have a couple of related mathematical questions that desperately need solving. Even Google doesn't know the answers! Here they are:

1. What is the probability of a standard Klondike Solitaire hand being unwinnable?

2. What is the best strategy for playing Klondike Solitaire in order to maximize your chance at winning the winnable hands?

My solitaire program keeps track of my aggregate playing statistics, and it looks like I win 15.6% of the hands I play. I wonder how much I could improve that number?

Come on, mathematical community! This problem has been staring you in the face for years (we have Microsoft to thank), but no one is tackling it!