Hand your friend a stack of twenty one playing cards. Instruct them to pick one out, without showing or telling you which card they chose, and to place the card back into the stack at random.
Deal the cards out in three columns, working row-by-row (1st column-2nd column-3rd column, 1-2-3, 1-2-3, etc.). You should have three columns of seven cards in front of you. Have your friend tell you which pile contains their card (without telling you which card it is, of course).
Gather the three columns into one stack of cards again, being sure to put the pile that holds their card in the middle of the three piles. For example, if the first pile contained their card, you could pick up the third pile first, then the first pile (containing the card) and then the second pile -- or the second pile, then the first, then the third. It is very important that the pile containing their card goes into the middle.
Repeat the past two steps two more times. When done, you will have dealt the cards out a total of 3 times.
If you have done the card trick correctly their card will be the 11th card in the pile of cards.
Your amazed friend may ask you how you did this. You can tell them it was magic... or you could explain the simple math that makes it work. Each time you deal out the cards you are dividing the placement of the card. By the 3rd time you have gotten the card into the middle of the pile. Thus you are able to tell where their card will be every time. The formula is Y=(X + 1)/2, where X is the number of cards and Y is the placement of the card in the pile after the 3rd deal. In this case, since X is 21, Y = 22/2 = 11.
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