# Guess the high card

1. Feb 15, 2010

### dilletante

Two decks of playing cards are combined to make a 104 card deck. On the face of each card is written a number. The numbers are all different and can be of any magnitude. You do not know the range of the numbers. The deck is shuffled and placed on the table face down.

Your task is to turn over the cards one by one until you think you have turned the card with the highest number, at which point you stop. If the number on your last card turned is the highest in the entire deck you win, otherwise you lose. Note that it has to be higher than any card previously turned as well as those left unseen.

You pay 5 dollars to play the game and if you win, you receive 20 dollars. Is this a profitable game to play?

2. Feb 15, 2010

### davee123

Looks like if you play with the correct strategy, you should be able to win somewhere between 1/3 and 2/5 of the time-- I'm not sure exactly what the "sweet spot" is for the strategy. But yes, that means that it is slightly profitable.

DaveE

3. Feb 16, 2010

### ƒ(x)

Turn over thirty-eight cards and then pick the next highest one