Who here is good at Math? (Faros and Stacked Decks)

[descartes]

This will be a bit long, but i'll try and be as clear as I can.

Your initial arrangement is different from new deck order. To prevent confusion, let us assume you number the cards 1-52 in their initial arrangement and given a number, you should know the name of the corresponding card. After 4 out faro shuffles, the sequence of numbers goes like this:

1 17 33 49 14 30 46 11 and so on.

You wanted to know how to find out the next card in the sequence.

1) Start with the number corresponding to one card (call this a).
2) To find the next card, add 16 to this number (b=a+16)
3) If the number b>52, take modulo with of b with 52 and add 1. i.e.,

c = (b mod 52) + 1

otherwise, c = b

4) The card corresponding to the number c gives you your answer.

example : take the number 17, which is the number corresponding to the second card in the stack. 17+16 = 33. c = 33 and therefore the next card is the one corresponding to this number.

However, if a = 49, then b = 65. c = (65 mod 52) + 1 = 14

BTW, you don't need to start in new deck order, so you could start with any stack and use this formula after 4 faro shuffles as long as you have memorized the initial arrangement exactly.

I hope this is clear, if you have any questions, send me a PM and I'll do my best to answer them.

P.S. You should refer to expert card technique also. It has a chapter devoted to the faro shuffle

 

[InfinitiM13]

I started this after you first posted and am still working on it. It is hard to explain, so I will probably make a video later about how to use the stack. Anyway, I switched the diamonds and hearts before my faros, so my hearts are your diamonds and vice versa.

If you dribble the pack, stop halfway, and look at the card on the bottom of the un-dribbled pile, you do 1, 2, and 3 to find the next ones except for the exceptions I will later talk about.

1. Find the next suit in the series (spade, club, heart, diamond, in that order. If it is diamond, go to spade)

2. If the suit of the card on the bottom of the un-dribbled pile is a spade, heart or club, add 3 to the value. If the suit is diamond, add 4 to the value. If the new value is over 13, subtract 13 to get the next card value.

3. If the first card is a face card, apply 1 with the other suit of the same color and 2 with 4 and 5 instead of 3 and 4.

The only exception is the King of diamonds, which comes before the ace of spades if the deck is cut.

Hope it helps.

 

[tally-ho]

or everyone can realize how simple it is by looking at my previous post.

 

[Wonder]

In Roberto Giobbi Card College Vol 3 he teachers a mathematical basis of the perfect faro shuffle, also more info on the mathermatics of faro shuffles are found in Expert Card Technique & The Collected Works Of Alex Elmsley, Vol 2. hope this helps