Topic: DeBruijn 52 cards 6 bit and non memorized
 Message: Posted by: glowball (Oct 16, 2018 01:35AM)
For those who do not have a memorized stack the below deck can be used to do this trick:
Spectator cuts this face down deck several times then deals 6 cards face down in a row on the table.
The magician can name the 6th card (the cards are not marked and the magician can be 10 feet away).

Construct this deck below (note that it has 5 necessary DUPLICATE CARDS):
-10H -KD -6D -3D -AD -10D +10S +10C +8C +QC +4C +5C
-5H -5D -7D +3S +AC -8H +QS -6H -JD -5D +2S
-AH -8D +4S +2C -9H -QD +6S -3H +9S +4C +10C
-KH -4D +7S +3C +9C -QH +4S +7C -JH +KS +6C +JC +KC
-4H +5S -7H +JS +5C

Note: orient the backs normally for the + cards (or use blue backed cards) these are your binary "1".
Note: orient the backs the reverse direction for the - cards (or use red backed cards) these are your binary "0".
Note: if you are using a "one way" backed deck then you will need two decks to construct the above 52 card deck (provides the 5 duplicate cards).

Note: if you are using a red backed deck and a blue backed deck then you will need four decks (two red and two blue) to construct the above 52 card deck (provides the 5 duplicate cards, need 2 red backed 5D and 2 blue backed 5C, 4S, 4C, 10C. Note that I use blue backed for the binary "1" and red backed for the binary "0").

Above deck legitimately has two of the following cards: +5C, -5D, +4S, +4C, +10C,
Mental rules while performing to determine the 6th card:
Look at the backs of the 6 cards on the table.
Evaluate the first 4 bits/card backs and use the binary value as follows:
If value is 4 or 14 then the 6th card is a 4.
If value is 5 or 15 then the 6th card is a 5.
If value ends in 0 (ie 0 or 10) then the 6th card is a 10.
Otherwise the binary value is the card number, examples: 1=Ace, 7=7, 8=8, 11=Jack, 12=Queen, 13=King.

Now look at the backs of the 5th and 6th cards and determine the suit as follows:
00=Diamonds
10=Hearts
11=Clubs

Note: due to the nature of this DeBruijn 52 and the Ace thru King scheme and 4 suit scheme the below 5 duplicates cards are necessary and 5 missing cards are necessary:
The 5 duplicates are 4C, 4S, 5D, 5C, 10C (yes these are needed).
The missing cards (OK) are AS, 2D, 2H, 8S, 9D.
 Message: Posted by: glowball (Oct 21, 2018 12:10AM)
A slight Improvement to this deck would be to replace the first 10 of clubs with the Ace of Spades. the advantage of this is that there's only four duplicate cards instead of 5 and also people might notice if one of the aces was missing and also this makes sure that your deck has four aces if you wanted to do any tricks that involved four Aces. Also it is very easy to remember that a 4 bit binary total of zero is the Ace of Spades.

Construct this deck below (note that it has 4 necessary DUPLICATE CARDS ie: 5C, 5D, 4S, 4C):
-10H -KD -6D -3D -AD -10D +10S +AS +8C +QC +4C +5C
-5H -5D -7D +3S +AC -8H +QS -6H -JD -5D +2S
-AH -8D +4S +2C -9H -QD +6S -3H +9S +4C +10C
-KH -4D +7S +3C +9C -QH +4S +7C -JH +KS +6C +JC +KC
-4H +5S -7H +JS +5C

The binary value rules to determine the 6th card now become:
Look at the backs of the 6 cards on the table.
Evaluate the first 4 bits/card backs and use the value as follows:
If value is 4 or 14 then the 6th card is a 4.
If value is 5 or 15 then the 6th card is a 5.
If value ends in 0 then the 6th card is the Ace of Spades.
Otherwise the binary value is the card number example: 1=ace, 2=2, ... 7=7, 8=8, 9=9, 10=10, 11=Jack, 12=Queen, 13=King.

Now look at the backs of the 5th and 6th cards and determine the suit as follows:
00=Diamonds
10=Hearts
11=Clubs

Note: you could say at the beginning of the trick "I am using part of a canasta deck" that way you are covered if someone notices any of the 4 duplicate cards.
Note: it could come in handy to do some other tricks by having a few duplicate card(s).
 Message: Posted by: glowball (Nov 12, 2018 09:44PM)
My prior post had slight error:
"If value ends in 0 then the 6th card is the Ace of Spades."
Correct statement is:
"If value is 0 then the 6th card is the Ace of Spades."
 Message: Posted by: D. Yoder (Dec 19, 2018 11:20AM)
I find this fascinating. I am not sure I will ever use this idea in the form of a 52 card deck, but I think doing it with a smaller deck of cards would be doable for my show and teaching. Thank you for sharing this.
 Message: Posted by: glowball (Dec 20, 2018 01:44PM)
D.Yoder,