Predicting the Reversed Cards

Effect:

The performer makes a prediction and writes a number on a piece of paper, which is given to an audience member for safekeeping. A deck of cards is shuffled, and a volunteer assists in the experiment. After some seemingly random card reversals, the number of reversed cards in the deck matches the prediction exactly. This is a Bob Hummer effect and is self working.

Performance Instructions:

Making the Prediction:
- The performer writes a number on a piece of paper (preferably between 18 and 30).
- This prediction is folded and handed to an audience member to keep until the end of the trick.
Creating Two Piles:
- The deck is shuffled freely.
- The performer asks a volunteer to cut off about 12 or so cards from the top of the deck and place them in a pile on the table.
- The volunteer then cuts off another 12 or so cards and places them in a second pile.
- The rest of the deck is set aside for now.
Reversing Cards (While the Performer’s Back is Turned):
- The performer turns around so they cannot see what happens next.
- The volunteer chooses any number of cards from anywhere in one of the piles and turns them face-up (they don’t have to be the top cards).
- They then turn over the same number of cards from anywhere in the second pile.
- Both piles are squared up neatly.
Reassembling the Deck:
- The volunteer picks either of the two piles and places it on top of the main deck.
- That deck is then handed back to the performer. The other small pile is still squared up on the table. The performer reminds the spectators that the performer has no way of knowing the number of cards that are face up.
The Secret Move:
- The performer takes the deck and secretly moves a specific number of cards:
  - Holding the deck behind their back, they count down the exact number of cards they wrote in their prediction.
  - These cards are then turned over and placed face-up somewhere inside the deck. The performer brings out the deck.
- The remaining pile (left on the table) is placed on top of the deck.
The Reveal:
- The assistant deals through the deck, dealing face down cards to one pile and face up cards to another. As the deal they count the face up cards to arrive at the total number of reversed cards.
- The prediction paper is opened and—amazingly—the number written matches the number of reversed cards in the deck!

Why the Trick Works: The Key Move Explained

At the moment the magician takes the deck, there are X reversed cards in the deck (and X reversed cards in the pile on the table). Now, let’s carefully analyze what happens when the magician takes “N” cards from the top and flips them.

Step 1: State of the Deck Before the Secret Move

At this point, the deck consists of:

X face-up cards spread somewhere throughout the deck the performer holds (because the spectator reversed “X” cards in each of two piles). The small pile on the table has X cards also.
The magician has written a prediction, “P”, which is greater than 2X.

Now the magician secretly takes the top “N” cards from the deck (where N is the prediction number).

Step 2: What is in the “N” Cards?

These “N” cards contain a mix of face-up and face-down cards.

X of those N cards are face-up, meaning the remaining N – X cards are face-down.

At this point:

X face-up cards
(N – X) face-down cards

Step 3: The Magician Reverses These “N” Cards

Now the magician flips the entire N-card block over before reinserting them into the deck.

The X face-up cards in this block now become face-down.
The N – X face-down cards now become face-up.

After reinserting these reversed cards into the deck, the new total number of face-up cards becomes (N-X). You then add the X face-up cards from the small packet on the table. Adding the small packet to the deck, the number of face up cards then is (N-X) + X. This is the same as X – X + N, which is equal to N.

Since N is the number written in the prediction, the trick always works perfectly!

Example

Let’s say the magician predicts 22.

Spectator’s Actions

They reverse X = 5 cards in one pile.
They reverse X = 5 cards in the second pile.
The deck now has 2X = 10 reversed cards in it.
They place one pile onto the deck for the magician, that part of the deck has X=5 reversed cards.

Magician’s Secret Move

The magician takes “N = 22” cards off the top of the deck.
In these 22 cards:
- X = 5 of them are face-up.
- N – X = 22 – 5 = 17 are face-down.
The magician flips the entire block of 22 cards over.
- The 5 face-up cards become face-down.
- The 17 face-down cards become face-up.
Now the total number of face-up cards in the whole deck is: (N-X) + X = 17 + 5 = 22
The spectator counts the reversed cards—it matches the prediction (22)!

Summary of the Secret

The spectator adds an even number of reversed cards (2X).
The magician removes N cards, containing X face-up and (N – X) face-down cards.
When these N cards are flipped, the balance of face-up and face-down shifts, making the total reversed cards equal N, which matches the prediction.

Final Thoughts

This principle is a beautiful use of hidden symmetry and parity control, a signature of Bob Hummer’s mathematical magic. The spectator believes they had free choices, but the magician secretly forces the final count with one clever move.