And for that matter Wei_Dai's solution, given his way of incorporating partial knowledge of one's intersection, is also correct

Thanks, this clarifies the state of the discussion. I was basically arguing against the assertion that it was not.

and also probably not the best way to generalize the problem because it basically asks, "what strategy should you pick, given that you have a probably t of not being an absent-minded driver, and a probability 1 - t of being an absent-minded driver?"

I don't think I understand this. The resulting agent is always stateless, so it is always an absent-minded driver.

Are you looking for a way of incorporating information "on-the-fly" that the original strategy couldn't account for? I could be missing something, but I don't see how this is possible. In order for some hint H to function as useful information, you need to have estimates for P(H|X) and P(H|Y) ahead of time. But with these estimates on hand, you'll have already incorporated them into your strategy. Therefore, your reaction to the observation of H or the lack thereof is already determined. And since the agent is stateless, the observation can't affect anything beyond that decision.

It seems that there is just "no room" for additional information to enter this problem except from the outside.