>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?

I have the vague impression that, because of too little information available, it is possible to arrange the game in such a way that the probability of any one card being the maximum in the series is 1/100 - despite the fact that I saw several cards previously. Therefore, I would not accept the game with 5 to 1 odds. I do not, however, have a proof that this is actually so.

(In actual practice, I never bet, but I like analyzing probabilities.)

Hilmar.