Three Word 13 Stories "Next Card" calculation to be used with a good looking tetradistic stack (a quicker way to determine the next card for a good looking stack. See further below under the paragraph title A BETTER WAY). But first some background info:

Apparently the Horacio Galasso stack/Gaspar Cardozo de Sequeira stack (early 1600s)/Selim Cid stack/Si Stebbins (1898) Stack are the mother of all tetradistic stacks. However it's rhythmic value progression and its alternating suit colors (red black red black red black all the way through) are undesirable to many magicians.

Therefore other tetradistic stacks such as the Eight Kings have been developed to break up the rhythmic value progression, but they can still have the red black red black alternating colors. Other variants have been developed to solve this alternating suit color problem.

However the more you make a tetradistic stack better looking the more complex it becomes to do a "next card" calculation quickly, especially determining the suit of the next card. The value of the next card is easily handled by the mnemonic story, it's the suit of the next card that is more difficult to calculate.

IMO there are two major calculations that are very desirable in a tetradistic formula stack:

1. The ability to know the position of every card ("acaan" feature).
2. Glimpse the bottom card of a cut deck and know the top card ("next card" feature).

Typically these two features use entirely different calculations and/or mnemonic stories.

Typically for a good looking tetradistic deck if it is easy to do one of the above features it will be more difficult to do the other feature.

For example the Si Stebbins is very easy at doing the "next card" feature but more difficult at doing the "acaan" feature.

The Harding Stack is the other way around ie: it is fairly easy to do the "acaan" feature but more difficult to do the "next card" feature (note: the Harding Stack is not a true tetradistic stack but it's imaginary deck is tetradistic).

The Eight Kings, Hungry !@#$%^& etc. tetradistic stacks tend to be easier doing the "next card" calculation but more difficult doing "acaan" calculations.

A BETTER WAY:

7S, QD, 8D, KC, 10H, 9C, AC, 3S, 6H, 5C, JS, 2H, 4D
7H, QS, 8S, KD, 10C, 9D, AD, 3H, 6C, 5D, JH, 2C, 4S
7C, QH, 8H, KS, 10D, 9S, AS, 3C, 6D, 5S, JC, 2D, 4H
7D, QC, 8C, KH, 10S, 9H, AH, 3D, 6S, 5H, JD, 2S, 4C

I'm going to use my Seven Queens V1 stack (immediately above) to explain this quicker way to calculate the next card, especially the suit of the next card (this 13 phrase technique can be used on other tetradistic stacks that might need it but of course greatly modified to fit the particular stack).

Instead of mentally thinking the entire Seven Queens story to know the value of the next card and thinking a separate mnemonic story to get the suit of the next card (JFK White House story in the Seven Queens stack), instead memorize each of the 13 sequencial next card pairs along with its suit descriptor rules. This "better way" scheme can use 4 special descriptor words one of which will be mentally placed between each card. These descriptor words are: "forward", "backward", "same", "color".

The 7 Queens mnemonic story for the 13 cards will now be:

"7 BACKWARD Queens SAME ate BACKWARD Kings BACKWARD 10 FORWARD 9 SAME Ace COLOR 3 FORWARD 6 FORWARD 5 COLOR Jack FORWARD 2 COLOR 4 COLOR 7".

Well, that's a little much to memorize, but we can simplify this by breaking it down into 13 little stories composed of the known card, descriptor, next card (first card value, descriptor how to change the suit, the second card value).

Seven Queens V1 better way 13 phrases with descriptor word between two cards:

"7 backward Queens"
"Queen same 8"
"8 backward Kings"
"King backward 10"
"10 forward 9"
"9 same Ace"
"Ace color 3"
"3 forward 6"
"6 forward 5"
"5 color Jack"
"Jack forward 2"
"2 color 4"
"4 color 7"

The word "forward" means the second card's suit is one notch forward (SHCD sequence) from the first card's suit.

The word "backward" means the second card's suit is one notch backward (SHCD sequence) from the first card's suit.

The word "same" means the second card's suit is the exact same suit as the first card's suit.

The word "color" means second card's suit is the same color suit but different from the first card's suit.

This memory method for doing a "next card" calculation will then be almost instant. Example: the Magician sees the Five of Hearts on the bottom of the cut deck. The "five" triggers the memory "5 color Jack" therefore the magician knows the top card is a Jack and it's the same "color" suit of the Five of Hearts therefore the Jack is the Jack of Diamonds.

I know what some of you are thinking: "That's a lot of memory work so why not bite the bullet and just memorize a Mnemonica or Aronson stack". I kind of agree, but once these 13 small phrases are mastered it should be easier and also quicker when doing a "next card" trick than with a mem deck.

Why should the "13 stories" method be quicker than a mem deck? Because most mem decks focus on acaan (knowing the position of any card and knowing the card for any position) and not as much on quickly knowing "next card". Even when the magician gets very good at knowing those positions the magician must go through an extra mental step when doing a "next card" trick IE: what number am I on, increment it by 1, now what is the card at that next position.

Instead of doing a mem deck increment by one: use a good looking tetradistic deck and have the 13 phrases above memorized (the Magician mentally goes directly to the next card).

I think the above 13 phrases type of memory method is superior to a mem deck when doing a "next card" calculation, however a mem deck is far superior when doing an acaan trick (a mem deck is much faster at knowing the position of a named card).

The trade off is that a calculation type of stack can be learned and performed in a few days whereas a mem deck typically takes a month or two to learn and perform.

Note that when memorizing a mem deck stack such as Aronson or Mnemonica the magician not only must learn the 52 card to number combinations, the magician must also memorize the 52 number to card combinations. That kind of means 104 combinations to memorize. Contrast that with what has to be learned/memorized with a tetradistic stack such as my Seven Queens stack: 13 stories also the 4 values associated with the four suits, also for acaan the magician must know the six Harry Riser type of pairs and the four offset numbers when doing mod 4 on the card value plus it's suit value.

The total things to memorize for the Seven Queens stack is 13 + 4 + 6 + 4 is 23 things vs 104 things to memorize for a mem deck. This is not to say that the Seven Queens stack is better than the Mnemonica stack anymore than saying a simple pickup truck is better than a Lexus. It all depends on who is using it and what it is being used for and how much you want to invest in it.
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Here are more complete mnemonic stories and visual techniques to recall the 13 phrases for the Seven Queens V1 stack.

Note that the word "crayon" translates to the word "color" which means the suit of the second card is the same color suit as the first card).

"7 backward Queens"
The Magnificent Seven (movie with Yul Brynner) are in the desert with their backs turned to the queen of England who is standing close to them.

"Queen same 8"
The letter Q as two smaller circles inside it (forming an 8) and there are two parallel straight lines instead of one (looks like an equal sign). Therefore think Q equals 8.

"8 backward Kings"
Imagine a giant vertical 8 on a football field with Kings backs to the 8.

"King backward 10"
When seeing a king playing card imagine he is holding a tin (10) of snuff behind his back.

"10 forward 9"
Star Trek The next generation has a relaxing area called "10 forward". Therefore imagine nine people sitting at a table.

"9 same Ace"
Cats are associated with the number nine (nine lives). Imagine a cat is the pilot of an airplane and that cat is an ace pilot. Or just visualize 9=A.

"Ace color 3"
Imagine the letter A being composed of three crayons.

"3 forward 6"
Imagine the 3 Andrew's sisters with their feet pointing forward (6 feet). Or choose your own body part (eyes, ears, arms, etc).

"6 forward 5"
Imagine a Nerf six gun revolver that only has five Nerf bullets and it revolves forward.

"5 color Jack"
Imagine the lower part of the number 5 being composed of crayons that form the letter J.

"Jack forward 2"
Imagine the letter J with two arrows coming out of the vertical part of the J pointing forward (left to right).

"2 color 4"
Imagine the number 2 with a vertical crayon (the middle of the crayon touches the right most horizontal line on the number 2) so it looks like the number four.

"4 color 7"
Imagine the number 4 having a crayon as the slanted portion and also a crayon is the vertical portion so that the two crayons form the number 7.

Final thoughts:
Each story has a first card value, then a descriptor, then a second card value. When doing a top card calculation the Magician should glimpse the bottom card and use the value of the bottom card to trigger the mental image of one of the above 13 stories (the bottom card value should bring to mind the first card value in the story).

The second card in the story is the top card value. The descriptor in the story tells how to mentally modify the suit of the bottom card to know the suit of the top card.

Example: the deck is cut and the magician glimpses the two of hearts on the bottom of the deck. The Magician visualizes a 2 with a vertical crayon making the number 4. Thus the magician knows the top card is a 4. The crayon signifies the "color" of the second card's suit is same color as the first card suit. Therefore the suit of the top card is a Diamond. Thus the top card is the Four of Diamonds.

Example: the deck is cut and the magician glimpses the King of Clubs on the bottom of the deck. The Magician visualizes a King with a tin of snuff behind his back. Thus the magician knows the top card is a 10. The "behind his back" signifies "backward one notch" (SHCD) for the suit. Hearts is backwards one notch from Clubs. Therefore the suit of the top card is a Heart. Thus the 10 of Hearts is the top card.

Example: the deck is cut and the magician glimpses the Six of Diamonds on the bottom of the deck. The Magician visualizes a Nerf Six gun with five Nerf bullets and rotating forward. Thus the magician knows the top card is a 5. The "forward" signifies "forward one notch" (SHCD) for the suit. Spades is forward one notch from Diamonds (wraps to Diamonds).. Therefore the suit of the top card is a Spade. Thus the 5 of Spades is the top card.

Note that the Si Stebbins stack does not need this technique because the value and suit of the next card are known by means of an easy formula (however the trade off is that the Si Stebbins stack looks very regimented).

Most of the Eight Kings stacks (and other tetradistic story stacks) do not need this 13-story method to calculate the next card because the main Eight Kings story will give the value of the next card and many of these stacks have a built-in formula to easily get the suit of the next card however there could be some benefit to adopting a 13 story method rather than having to mentally recite the Eight Kings story each time to know the next card.

Also note that some of these stacks are primarily "next card" calculation stacks, but do not easily do the acaan calculation whereas the Seven Queens stack does both.