Consider the single-player version of Memory, where you try to uncover matching pairs of cards by flipping over two at a time. If they match, remove them -- if not, put them back. And assume you have a perfect memory and play perfectly. Given p pairs of cards (n=2p cards total), how many turns does it take, in expectation, to find all the matches? We have a recursive function that can efficiently get the answer for any specific number of cards but have not found a closed form.

Will we find it?

Here's our ongoing progress: https://forum.beeminder.com/t/matching-game-perfect-play/10346