Uncle Billy Magic Card Trick

 

Give your guest(s) for whom you are demonstrating the magic a standard deck of 52 cards. Instruct them to shuffle the cards.

Construction of piles

Ask your guest to deal the first card face up. If the card is a 10 or face card, return the card to the bottom of the deck. For any other card, Ace to 9, have them deal additional cards face up on the first card. The number of cards added equals 10 minus the value of the first card. So, if the first card is 8, 2 additional cards should be added to that pile. If the first card is an Ace, count it as a one and add nine cards face up to its pile.

An 8 was dealt, so 2 more cards were added (10 - 8 = 2)

A king was dealt so it was returned to the deck.

Once you see your guest understands the construction of the piles, you can turn your back and allow them to continue the process until they have used all the cards in the deck. Your guest should be able to construct about eight piles (could be more or less depending on the starting cards). Note, your guest might be left with a few unused cards as they reach the end of the deck. Ask them to return these cards to you.

Nine piles were constructed in this example.

Two cards were left over unused. Returned to magician.

All the piles are turned over face down. Their original starting cards should now be on top.

Selection of three piles

The next step, while you are still facing away from your guest, ask them to turn over all the piles so each is face down and each pile’s first card should now be on top, also face down. Ask your guest to select any three of the piles and to collect all the cards from the unselected piles and return these cards to you.

The three selected piles on top and all the other cards returned to the magician.

From the stub of cards (the few unused cards from the pile construction and the unselected piles) you have, count off 19 cards and hand these cards to your guest. Instruct your guest to distribute the 19 cards to the bottom of the three selected piles. They can be distributed in any method. Explain that the purpose of this step is so one cannot view a pile and guessing what the top card is by estimating the size of the pile.

19 cards returned to the guest.

The 19 cards are split between the 3 piles and placed on the bottom of the piles.

The 3 piles straightened up.

Completing the trick

You can now face your guest (but you could also continue the trick with your back turned). Ask your guest to pick one pile. Your job will be to determine the value of that pile’s top card. Ask your guest to reveal the other top card of the other top piles. From you remain stub of cards, count off a number of cards equal to the sum of the two exposed cards. Now count the number of cards remaining in the stub and that will be the value of the unexposed card. Have your guest turn it over to confirm the answer.

Two top cards exposed, and a matching number of cards dealt off (five cards for the 5, two for the 2)

Three cards remain with the magician, and so it is announced the unexposed card is a 3.

Confirmation of the trick.

How does it work

We need to complete a reconciliation of the deck’s 52 cards, to show that number of cards remaining in the stub, X, will equal the value of the unexposed top card of the final pile.

52         Starting Deck

-3          The three top cards of the three selected piles

-19        The 19 cards you counted off the stub

-20        For the two exposed piles, let the top card values be A and B. For each pile's construction, (10 - A) and (10 – B) cards were first added to those piles. Then, at the end of the trick you summed A and B and counted off those cards. So (10 – A) + (10 – B) + A + B = 20.

52 – 3 – 19 – 20 = 10 cards remaining to reconcile. As we did above, let X be the number of cards remaining in your stub. Therefore, the number of cards originally under the hidden card is (10 – X). This number plus the value of the unexposed card is also 10 as that is how the original pile was constructed. So, we have (10 – Value of top card) = (10 – X), therefore X = Value of the top card.

I learned this trick from my uncle Billy, William Young. He was a great sports handicapper and worked with Jimmy (The Greek) Synder for many years - Jimmy Snyder (sports commentator) - Wikipedia. Sports bettors and other gamblers have to be mindful of the Kelly Bet Criterion discussed in this other post - Math Vacation: The Kelly Betting Criterion (jamesmacmath.blogspot.com).