Card Tricks

[Mike PSS]

There's quite a few card tricks based on math/sets. One of these is the 3 Pile Card Trick.
http://www.pleacher.com/mp/puzzles/tricks/piles3.html

Take a well shuffled deck of cards.
Deal out a card and add to its pip value enough cards to add to 13.
(Jack = 11, Queen = 12, King = 13)
In other words, turn over the first card. Count out enough cards to 13. Then put the original card back on top of that pile face down.
Do the same for another pile and continue until you cannot deal another pile.
Keep remaining cards in your hand.
Have someone pick any three of the piles.
Return all other piles to the cards in your hand.
Turn over the top cards on any 2 of the 3 piles.
From the cards in the deck, deal out 10 cards plus a number equal to each of the turned up cards.
Count the number of cards left. Announce that number.
Turn up the card on the top of the third pile.

So, I learned the trick making piles adding up to 10 and burrying the face cards and 10's when they appeared. Then the math adds up to counting out 19 cards, the sum of two piles revealed, and the remainder the hidden card.

If you do the trick with a bunch of hand waving, humming/hawing, a few pauses while concentrating on the back of a card or two; then the suspects think its an illusion trick or sleight of hand instead of just counting cards. Since most people are math challenged they don't pick up on how easy it is.

I then challenge someone to a game of 52 pick-up as long as they go first.


Any other card count tricks people have learned?

[Brother Daniel]

I can't make head or tail of those instructions.

[Mike PSS]

I can't make head or tail of those instructions.

Turn one card over (say a 4) and then pile cards on top of the four, counting out to 13 (5,6,7,...). Turn the pile over so the 4 is on top (face down).

Repeat and make as many piles as you can, but the last incomplete pile of cards that don't make it to 13 (if it exists, the last pile may just consume all the cards) just hold onto those cards.

Choose three piles, gather all the other piles cards in your hand.

Turn over two top cards. Add them together.

With the cards in your hand just count out 10 cards, then the sum of the two cards flipped over.

The number of cards remaining in your hand is the value of the card not turned over.

[Mike PSS]

I can't make head or tail of those instructions.

Would you like to play 52 pick-up? You, of course, would go first.

[Brother Daniel]

[instructions snipped]...
The number of cards remaining in your hand is the value of the card not turned over.

Ok, makes sense now. But even with the math-challenged, I would expect them to object that I had memorized the starter cards of each pile (i.e. the cards that end up on top of each pile when they're turned face down). Which wouldn't be terribly hard to do. So I wouldn't expect this to look impressive.

Would you like to play 52 pick-up? You, of course, would go first.

That means that I get to throw the cards and make you pick them up, right?

[Mike PSS]

Ok, makes sense now. But even with the math-challenged, I would expect them to object that I had memorized the starter cards of each pile (i.e. the cards that end up on top of each pile when they're turned face down). Which wouldn't be terribly hard to do. So I wouldn't expect this to look impressive.

I've had that objection in the past and all I did was have them move the piles (NOT shuffle them) around randomly while I'm not looking and then choose three and then turn over the top two cards while holding the third pile in their hands (NOT shuffling that pile either of course) while only revealing the value of the two top cards.

You can come up with all sorts of illusionist or "magic" types of movements and actions as long as the top cards don't get disturbed, they are the only ones revealed and the remaining cards in the piles selected don't get mixed into the pile in your hand.

Try it out a couple times and you find out that there are a hundred ways to hide the fact that all you're doing is counting cards.

[Brother Daniel]

ok, that makes sense.

[SkepticTank]

Not card counting, but I guess it's a math thing. I haven't figured out why it works, but the first trick I learned.

Let someone pick a card and insert it randomly back into the deck (you can even allow a shuffle at this point).

Deal out the cards in 3 columns alternating 1-2-3

Tell the person to select which column their card resides in

Pick up the columns with the selected column always 2nd (not sure on this detail it's been a few decades since I did this trick)

Repeat the column deal/select/pick up twice

The chosen card will always be in position #19? in the deck.

eta:

Simple 3-row magic card trick - YouTube

Simple 3-row magic card trick - YouTube

but he did it with a 21 card deck.

[schneibler elf]

I used to know that one using 21 cards

[SkepticTank]

I used to know that one using 21 cards

Yeah, I may be mis-remembering the way I learned it.

[Brother Daniel]

Yeah, with a 21-card deck, you get 3 columns of 7. By laying the cards out and then picking up the selected column 2nd, you're just rearranging the deck so that:

if the chosen card was in position 1, 2, or 3, it goes to position 8
if it was in position 4, 5, or 6, it goes to position 9
7, 8, 9 goes to 10
10, 11, 12 goes to 11
13, 14, 15 goes to 12
16, 17, 18 goes to 13
19, 20, 21 goes to 14

so three iterations of this procedure puts it in position 11, no matter where it started.

[Mike PSS]

I had forgotten that simple trick.

Largest single deck is 51 cards (17 per row).

1,2,3 goes to 18
4,5,6 goes to 19
7,8,9 goes to 20
10,11,12 goes to 21
13,14,15 goes to 22
16,17,18 goes to 23
19,20,21 goes to 24
22,23,24 goes to 25
25,26,27 goes to 26
28,29,30 goes to 27
31,32,33 goes to 28
34,35,36 goes to 29
37,38,39 goes to 30
40,41,42 goes to 31
43,44,45 goes to 32
46,47,48 goes to 33
49,50,51 goes to 34

The trick only works with an odd number of cards per column.

The center number of the string is your end position number; which is ROUNDUP(1.5 * column length).

Number of iterations to reach that center number is still MAX 3.

ETA: Which means ST's memory is flawed since no number of odd rows result in position 19 being the chosen card.

[Brother Daniel]

With 51 cards, it looks like it takes 4 iterations to be sure that the chosen card is in position 26.

[Mike PSS]

With 51 cards, it looks like it takes 4 iterations to be sure that the chosen card is in position 26.

Oooops.
Yup, I forgot to include the initial point. Instead I just counted the moves.

[Brother Daniel]

Kinda looks like the number of iterations required (to get the chosen card to the centre position) is

roundup( log₃ (number of cards in deck) )


but obviously I haven't proved it.