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 Question by hoodat)

Since the world expected appears here, I think that the player wishes over the long run to minimize his total and therefore average, number of turns to complete the grid. Thus in the n=2 case with 4 cards, after failing to match on the first try I'd expect the player to choose one of the known and one of the unknowns. 

Posted by Charlie on 2017-06-02 04:57:16