Magic Trick - Red / Black

 

My favorite magic tricks are those that require no sleight of hand. Many tricks use math to complete the trick. This trick and others outlined by this blog also use math.

Set-up

Use a standard 52-card deck of cards. Shuffle the deck and allow your guest to shuffle the deck. Demonstrate to your guest what you want them to do.

Deal the first card face up on the table. If the card is red (hearts or diamonds), place the card face up on the right or if it is black (spades or clubs), place the card face up on the left. Deal the second card face down in a new pile directly above where you placed the first card. Repeat this a few times until your guest understands the process. Your guest can continue with this process or offer them to re-shuffle and start from the beginning of the deck. 

 

Your guest continues with this process until all 52 cards have been dealt. There will be two face up piles of red cards (on the right) and black cards (on the left) and two face down piles above the two face up piles.

Next, ask your guest and other people present if they think there are more red cards in the face down pile on the right than black face down cards on the left. Remind your guests that cards dealt face down in either pile are independent of the card dealt prior face up. Your guests may have noticed a discrepancy in the number of red and black cards dealt up. This is common and encourage the discussion of how this might impact the number of red and black cards in the face down piles.

Complete the trick

Announce to your group that you project the number of red cards in the right face down pile is the same as the number of black cards in the left face down pile. 

Ask your guest to flip over the two piles of face down cards and count the number of red and black cards in each pile to confirm your prediction that the number of red cards in the right face down pile matches the number of black face down cards in the left pile.

Variation

After the deck has been dealt into the four piles, ask another person in the audience to give a number between one and seven. Have the guest who was dealing, switch that number of cards from the two face down piles with each other.

How does this trick work?

After all the cards are dealt out, we have four piles with two face up piles of red and black cards and two piles of face down cards.

Designate the number of face up red cards as X. There will be an equal number (X) of face down cards on the right. Designate the number of red cards in the face down pile as R. Therefore, the number of black cards in the right face down pile will be X-R.

The number of face up black cards on the left will be 26-X (this is actually 52 total cards minus 2 times the number of cards dealt on the right hand side).

There are a total 26 black cards in the deck so the number of black cards on the left face down side will equal 26 minus the black cards dealt face up (26-X) and minus the black cards dealt face up in the right pile (X-R).

The final result of the black card dealt face down on the left hand side (B), will be:

B = 26 – (X-R) – (26 – X) or with the 26 and X canceling,

B = R

Regarding the variation of switching an equal number of cards in the right and left face down piles, the equation remains the same because trading the cards in the face down piles doesn’t impact the final equation of B = 26 – (X-R) – (26 – X).