Open problems concerning card games

I’m glad to say that editorial work on the Princeton Companion is within a whisker of being completed (about three articles remain to be edited), so although I don’t quite feel that I have the leisure to give proper attention to this blog, which will be obvious from some of the messages that I haven’t got round to deleting, I can at least write a quick post. It starts with a conversation I had a couple of years ago. I was waiting for a plane to take me from Mykonos to Athens. The plane was severely delayed, but the situation could have been a lot worse as I had Persi Diaconis for company. He told me the not very surprising fact that it was not known what the probability of a win is in the game known as Patience in the UK and Solitaire in the US. (I’m talking about the one where you start by putting down a row of seven cards with just the first one face up, then on top of all but this first one a row of six cards with just the first one face up, and so on.) To be clear about the probability he is asking for, he simplifies the game by letting you see what all the cards are, so that you can play optimally and don’t have to worry about probabilities.