I had to explain a self-working card trick for math class. This is what I wrote up and handed in. I just thought i would share it with you guys, who knows, maybe you'll use the trick.

PROBLEM: Explain why the following card trick always works:
The Effect: A magician writes a prediction on a piece of paper. He then takes twelve cards out of a shuffled deck and has four of them put down face-up. The remaining eight cards are discarded or put on the bottom of the deck. The magician then explains that he will deal cards down to make each card equal ten ( i.e., four cards dealt on top of a 6), and that all face cards equal 10 and Aces are ones. After this he says he made a mistake that he was thinking of another trick. All the cards he dealt down are discarded or put on the bottom of the deck. He then says he was supposed to deal down cards equal to the sum of all four face up cards. The last card he puts down matches his prediction.
The Secret: The prediction is the bottom card. The rest is self working.
WHY IT WORKS: You must have a full deck of 52 cards for this to work by the method described, but at the end I will give a way with an incomplete deck. It doesn’t matter if you have duplicates; you could even have a deck that’s all one type of card and this would work. In the following explanation, the term “active cardsâ€