Hi Daniel,

I would not play this game.

Reason -- there are several crucial pieces of information necessary to properly compute the odds:
a) I don't know if you shuffle the deck between each play of the game.
b) "when I think the last flipped card has the highest value printed on it" -- highest value compared to WHAT? If I'm supposed to determine whether a value could be a possible ceiling value, I need to know what I'm comparing it against.
c) the range of available values on the 100 cards (if I have no idea what the range is, I have no way of determining whether or not the last flipped card is in the upper range of possibilities, so it's a complete guessing game)
d) The number of cards, given your description, should not affect the odds -- since it's a wild guess what *ANY* of the cards have for an identifier, the odds are 99 to 1 each time if you shuffle the deck before each play.
e) I have no idea if YOU know what the range of values for the cards are (if you know and I don't, that puts you at a distinct advantage much greater than five-to-one).

I would play this game if:
1) The range of cards were specified (ie, 1 to 100).
2) The game were modified to compare the last flipped card TO THE (n'th) FACE-DOWN CARD AFTER the last flipped card (for instance, flip cards until I stop, burn three cards, and compare the fourth to my card)
3) The used cards were discarded until a shuffle and the deck was shuffled when no -less- than 60% of the deck was played.

The strategy for that game would be relatively simple -- make small bets for the first 25% of the game, keeping a point count score for the cards that had been removed from the deck. Since you would know the total number of points still available in the deck at any given moment, you could then determine what your "best stop" card would be and make larger bets as that stop card became easier to determine.

HTH.

>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?