Calculate what the chances are that the second highest card has already been turned over.
Technique: Once you've reached halfway, if you see a card that's higher than all the other cards, tell the dealer to stop. If you take note of the second highest card in the first half of the deck. and then pick any card higher than the this card in the second half of the deck you will have a 1/4 chance of selecting the highest card. Explanation: There is a 1/2 chance that the second highest card is in the first half of the deck. There is a 1/2 chance that the highest card is in the second half of the deck. Therefore there is a (1/2)*(1/2) = 1/4 chance that both these conditions hold true. If both these conditions hold true you will always pick out the highest card. Amazingly the outcome has nothing to do with the size of the deck!