10 cards with identical backs are face down on a table. Each card face matches exactly one of the other card faces. The cards are in a random sequence. A turn consists of choosing 2 cards, simultaneously reversing them so that they are face up, discarding them if they match, and turning them face down if they do not match. The game ends when all cards are discarded.
a) If you have perfect memory, and an efficient strategy, then what is the expected number of turns in the 10 card game?
b) What is the expected number of turns if instead there are 2n cards in the starting tableaux, with each card matching exactly one other?
(In reply to re: computer discovery
I am also curious about the expected value with the usual rule of memory. I have not worked out the expected value for that game, but if I do I will post it as a separate problem.
I have an analytical solution for this game, and I confirm that Charlie's formula is correct. I will hold off another day or two before posting that solution.