# Belchou’s Aces – an oldie but a fun mathematical card trick!

In Mathematics Magic and Mystery by Martin Gardner, he describes a trick that was published in an earlier publication in 1939. This one is easy to set up and surprising, as you can have a friend run the whole trick with a few simple instructions, no sleight of hand! Here’s how it works:

The deck is split into 4 parts, part A, B, C, D. Your friend picks up A, sets 3 face down cards back in its place, and one card face down in each in other piles, and sets the rest of A in place over the 3 cards in spot A.

Picking up B, they will set 3 face down cards back on B, one card each above other quarters of the deck A, C, D and set the rest of B back on B.

The same for C, and then D.

After this shuffle-around, you will look uncover the top of A,B,C,D are all aces (or whatever your favorite suit is that you set up first!)

## The Setup

To set this trick you simply start with the 4 aces or target cards at the top of the deck. If you shuffle first don’t shuffle the first cards – this way they will be the top of D:

Part D is processed at the end and at that point will have three cards from the others:

Setting back three top cards to the spot D makes it the original top cards in D, and then you set the three cards to the top of A,B,C making all of them the same type!

## Variations

You can also run this trick with 5 roughly equal segments of the deck. Start with 5 clubs, for example, then pick up and set down 4, set down 4 in the other 4, repeat for each segment of the deck. The top 5 will be the original top 5. Move these 4 to the other 4 segments of the deck and now you have all clubs! This would work for any other numbers N with (N-1) moved in place and (N-1) moved to other segments of the deck, but 5 is the max for the standard deck.