After developing a 4-digit system, I was wondering if it would be possible to create a 3-card system to accompany it. I’m not talking about a “fake” 3-card system where there are actually 2 images (one for ranks and another for suits). I mean a “true” 3-card system. More precisely, I’m talking about a block system, like the shadow or the Double-2-Block system, because having 140,608 images would be impossible.
The following is what may make 4-digit systems common in the future:
First, we need to create something that I named “Formation Code.” This number is a 1- or 2-digit number that encodes what, if any, cards in the triple are picture cards (P) and what cards are number cards (#).
FORMATION CODE
In other words:
0: there is no picture card;
1: there is one picture card;
80: there are two picture cards together in the end;
81: there are two picture cards together in the beginning;
90: there are two picture cards separated;
91: there are three picture cards.
We need a simple way of representing the ranks of number cards using digits:
NUMBER CARDS CODES
To represent picture cards, we are going to encode by pairs:
PICTURE CARDS CODES
The columns may represent either the position of the picture card in the triple or the second picture card’s rank. For instance:
the pair “JQ” is 8
the triple “K49” has 7 as K’s number
That means that, if we don’t have a pair of cards, we can still use this table to encode both the picture card’s rank and its position in the triple. Notice that, if there are two picture cards, we can’t know where the pair is located based on the code alone; in these cases, the formation code is essential.
Moreover, it doesn’t matter if there is a number card between the picture cards. “1st Card” means “1st picture card in the triple” while “2nd card” means “2nd picture card in the triple.”
Example:
The picture cards in the triple Q2K are represented by 6
Now I’m going to explain how each triple of ranks can be encoded using a 4-digit number. One of the most important things is the following:
PRIORITY OF CODES:
- Formation code;
- Picture card’s code;
- Number card’s code (in order).
Examples:
786 is 0786 (Formation code: 0)
6Q2 is 1562 (Formation code=1 and Q=5 in this case)
10JK is 8030 (Formation code=80 and JK=3)
QJ3 is 8143 (Formation code=81 and QJ=4)
KAJ is 9071 (Formation code=90 and KJ=7)
For triples made exclusively of picture cards, the first one will be represented as if it were alone while the other two will be encoded as a pair:
KQJ is 9174 (Formation code=91, K in the 1st position = 7, and QJ=4)
Now we can encode the ranks. What about the suits? Here is where I needed to create multiple blocks to encode information. Only the first suit has blocks that modify the final number. The other suits have blocks that change how the image will be stored in the memory palace.
For the first card’s suit, we are going to modify the formation code. The following is the conversion table:
FORMATION CODE CONVERSION
The table of formation codes that I showed in the beginning was incomplete, sorry. That one only contained the codes for when the first suit is 
. Don’t worry, the other codes aren’t difficult to memorize. They are just the left code plus 2. Also, notice that for the codes that have 2 digits, only the units change.
You can also give each suit a value (=0, 
=1, 
=2, and 
=3) and apply the following formula for the formation code:
Formation code = 's formation code + 2*Suit value
Now we can convert each triple of ranks (and the first suit) into a 4-digit number.
Examples:
J 4K is 9234 (Formation code is 90 + 2 * 1 = 92 and JK=3)
4 QJ is 8644 (Formation code is 80 + 2 * 3 = 86 and QJ=4)
Q JK is 9543 (Formation code is 91 + 2 * 2 = 95, Q=4, JK=3)
The truly difficult part comes now: how to encode the remaining 16 suit combinations? I’m going to propose a standard solution, but I’m going to propose alternative strategies as well. You may pick the one that you prefer.
First, let’s name the strategies:
Sublocus Strategy: this strategy consists of dividing every locus of the memory palace into 2 (2-sublocus strategy) or 4 subloci (4-sublocus strategy). For instance, you may divide each locus into wall and floor, into right and left sides, or left side of the wall, right side of the wall, left side of the floor, and right side of the floor. This requires prior planning of the memory palace, especially if you want to divide it into 4 parts. In the 2-sublocus strategy, put the image inside the first sublocus if the second suit is or ; put the image inside the second sublocus if the second suit is or . In 4-sublocus strategy, put the image inside the first sublocus if the second suit is , inside the second sublocus if it’s , inside the third sublocus if it’s , and inside the fourth sublocus if it’s .
Agent-Observer Strategy: we mostly imagine ourselves as observers instead of agents when memorizing. However, we can also imagine ourselves interacting with the images inside the locus. This strategy can be applied in two ways: Current-Agent-Observer or Next-Agent-Observer. In the former, we do the following: if the second suit is red, then I’m an agent interacting with the current image; if the second suit is black, then I’m an observer (I don’t interact with the current image). In the latter, we do differently: if the third suit is red, then I’m going to be an agent, interacting with the next image; if the third suit is black, then I’m going to be an observer, not interacting with the next image.
Variable Image Stacking: this is the only strategy not invented by me. It was invented by Johannes Mallow. In our context, It consists of putting the image in the current locus and going to the next one if the third suit is red; otherwise, keep putting images in the same locus;
Variable Story Stacking: most of us memorize by creating stories with our images in the memory palace. Some people create continuous stories (like legendary Ben Pridmore/ @Zoomy, who has commented on this forum that the loci work just as backgrounds for him). Others may cut the story at the end of locus. Some may even cut the story at the middle of the locus. Since the end of the story is independent of the end of the locus, we can use it to encode information: if the third suit is or , then stop the story; if the third suit is or , then keep the story going.
Now that you understand each strategy, you can choose them according to your preferences to encode the remaining 16 suit combinations. I would recommend three possible combinations. The orders were chosen to make visualization as fast as possible.
16 SUIT BLOCKS
In my opinion, the second option is the best one because it isn’t too rigid and wouldn’t require me to divide my loci into too small spaces, but other people may disagree.
ENCODING
For any of the options, you should start by spotting the first suit. It will determine the list of formation codes to use. After that, read the ranks of the cards and convert them into a 4-digit number/image. Afterward, you need to apply the chosen strategy(ies) to encode the second suit. Finally, the strategies for the third suit tell you how to behave in the next locus, like “stay in the same locus” or “keep the story going.”
DECODING
Decode the image into a triple of ranks and the first suit. Later, try to recover the second suit by applying the opposite reasoning to your chosen strategy(ies). Finally, analyze the next locus to decode the third suit.
In conclusion, this system requires 8,788 images (3.25 times as many as the Ben System’s and 6.5 times as many as the Shadow System). On average, this method needs just 8.67 loci while 2-card systems usually need 13. In other words, there is a 50% improvement in card per image and a 33% decrease in number of loci.
I would love to know what you think about this system. Do you think it is possible to apply it? Would it be slower or faster? Could this system make 4-digit systems worth it?
