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 computer discovery
Very interesting. I'll try to find time to try proving this.
I wonder how much lower the e.v. would be with the usual rule of memory: You turn two cards on a turn but one at a time. So if the first turned card matches one you've seen you take its twin for your second card. (If not, strategy would be uncover another unknown card.)
Posted by Jer
on 2017-05-31 21:18:03