Daniel,

Since nobody is really giving a stab at it, I will. There is a 50% chance that the largest card is in the last half of the deck. There is also a 50% chance that the second largest card is in the first half of the deck.

My strategy would be this:

Turn up the first 50 cards, and remember the highest number, lets call the value 'X'. Continuing with the 51st card, I would stop on the first card that has a higher value than 'X'.

The odds would be the same no matter how big the deck.

Statistically, I'm not sure what the real chances of success are using this method...but I think may be 1 out of 4 chance. If that is true, I would play the game at 5 to 1 odds.

>Note: Please do not post the answer immediately if you know the answer. I want the UTers to put their thinking caps on.
>
>Given a deck of 100 cards where each card is uniquely identified by a number printed on the card (no range specified). Would you play this game?
>
>The game:
>I shuffle the cards and put them face down in front of you. You flip the cards face up one at a time and must say stop when you think the last flipped card has the highest value printed on it. I give you 5 to 1 odds.
>
>Is this a fair game? What if I included 1000, or even 1,000,000 cards in the deck? What odds must I give you in order to convince you to play the game? What strategy would you use?