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:

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

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A
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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.

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