
                              CARD GAME HELP

     Here's a card game you can try with your friends.  You'll be the dealer,
and you'll know the exact odds of winning.  Sound good?  Read on.

     You'll be playing with only 10 cards numbered ace through 10.  (Suits
are unimportant).  Have your friend choose 2 numbers from 1 through 10.  
Next have him shuffle the 10 cards without looking at them.  Then have him
remove 5 out of these 10 cards and turn them over.  If BOTH of the 2 numbers
he chose are included in the 5 cards he turned over, then he wins.  Otherwise,
you win.

     You're probably thinking that the odds of you losing your shirt over a
period of time are pretty good.  I think you're going to be in for a nice 
surprise.  Let's figure the odds:

     The program will ask you 3 questions:

   Question 1: Enter total number of cards to choose from.  In our first 
example the answer to this question is 10, because we used 10 cards to play.

   Question 2: Enter number of cards to be turned over.  The answer to this
question is 5, because we asked our pal to turn over 5 cards out of the 10.

   Question 3: Enter number of cards picked.  The answer to this question
is 2, because we asked him to pick 2 cards out of the 10 in order for him
to win.

    After answering these questions, the program will tell you the exact     
chances of HIM winning.  In our example the answer is 1 out of 4.50.  (Or
3 1/2 to 1.  This is figured out by subtracting the 1 from the 4.50).  But
what does this mean?  What it means is that if you were to give him odds of
3 1/2 to 1, using the numbers we used in our example you would more than 
likely break even over an extended period of time.
    However, and here's where it gets interesting, if you gave him odds of
say, 2 to 1 (which he is likely to accept gladly), you would most likely
clean up in the long run!  That's the advantage of knowing the odds ahead
of time.  

    
    Here's another variation on the game.  Instead of asking the player to
pick a number from 1 to 10, you can have him use all the picture cards in
the deck.  (There are a total of 12).
    Once the 12 cards are shuffled, have him name 3 of them; for example the
King of Hearts, the Jack of Diamonds, and the Jack of Spades.  Next, have him
turn over any 8 of the 12 cards.  If ALL 3 of the cards he named are now face
up, then he wins.  Other wise you win.

    Let's figure the odds.  The answers to the 3 questions would be:

   Question 1: 12

   Question 2:  8

   Question 3:  3

    
The program tells us that the odds of THE PLAYER winning are 1 out of 3.93 (or
2.93 to 1).  If you offer 3 to 2 or even 2 to 1 odds, you'll still win in the 
long run.


     Well, 
        
                          GOOD LUCK!!!!!






   