This may not be the next Monty Hall problem, but it is an interesting one. Mohan Srivastava, a geological statistician, cracked the Toronto Scratch-and-Win lotto. The article describes how to choose winning tickets but is vague on the algorithm that generated the cards. I’m going to take a crack at it and post my solution another time. (Poisson process?)
But what I really liked about the article was Srivastava’s approach to solving the problem. He looked for the underlying mechanism that generated the data. While a good understanding of subject matter can help a statistician know how to frame research questions, sometimes context can cloud the solution. If you can see past the subject matter you might just find that the solution for telling which mine shafts are most likely to have gold is the same as identifying winning lottery tickets.