I run site with thousands of solitaire games played a day. We tried to built an AI that would allow us to understand what hands were winnable or not. It turns out, like many of the responses, that there are so many permutations to win or lose a solitaire game that an AI to detect a winnable or non-winnable game is extremely difficult to build and requires significant processing power. We weren't able to succeed in building it.
Now, we simply leverage our user data to find which games are winnable, and offer that as option for players who want to play winnable only games. Otherwise, they can choose a random game. I would recommend trying something similar!