Seven Queens mod 4 acaan calculation

I have posted more details to this under secret sessions and some info under shuffled not stirred but I wanted you math guys to have some visibility to this and perhaps you have knowledge of this mod 4 technique being used on a tetradistic stack before? Thanks.

The main essence of this calculation is:
Add the card value and it's suit then mod 4 that number thus you should know the 0, 13, 26, 39 factor.
Then just add in the value of the named card's paired twin card.

I have been looking for a non-memorized stack that meets the following three criteria (for my magician friends that do not wish to memorize a 52 card deck):

My (glowball) Criteria for a non-mem deck:
1. Has reasonable randomness look ie: better than a Si Stebbins.
2. Can do an acaan (any card) calculation a little easier and faster than the Harding stack.
3. Can fairly quickly calculate what the next card is from a known card identity.

Off the top of my head the stack that comes immediately to mind is the Osterlind Breakthrough stack which is quite close to meeting my three criteria however I would like the calculations to be a little bit easier than the Breakthrough stack.

A tetradistic stack is fine as long as it meets the three criteria, especially criteria 1.

I recently came up with this system (won't be surprised if someone else has done this long ago) that I believe meets the three criteria. The unique part of this system is a special way of using the mod 4 calculation.

This is a tetradistic arrangement with Harry Riser type pairs where the paired values increment by one from Ace to two to three etc thru King (ie: 1 thru 13) and different suits (somewhat like Eight Kings stack). Nothing new here. But here is where my mod 4 technique comes into play.

Making mod 4 work:
Thought process and creating this stack:
Hopefully the first group of 13 cards could all mod 4 to a result of the same value and then the second group of 13 could mod 4 to a different value (all the same mod 4 value within the group) and so on for the third group of 13 and then for the fourth group of 13.

If this could be done then it would be a simple matter of associating one of four starting factors (0, 13, 26, 39) with each group and then adding the paired card value and bingo we have the position of the spectator stated card. Pretty easy.

Let's say the following is the sequence of the 13 random looking cards but their suits have not yet been determined for our ideal stack.
7, Q, 8, K, 10, 9, A, 3, 6, 5, J, 2, 4

I did a lot of experimenting and found the simple solution of adding the suit value to the card value to come up with a number to apply the mod 4.
I use SHoCkeD for the values of the suits:

Spades are 1 (Spade has one point)
Hearts are 2 (Hearts have two lobes)
Clubs are 3 (clubs have three lobes)
Diamonds are 4 (Diamonds have four points)

Let's say that our four groups of 13 cards that we call them:
Group 0
Group 1
Group 2
Group 3

For purposes of this post the term "mod 4" will simply mean the remainder value when dividing some number by the constant 4.

I'll explain why group 0 is listed first but for now let's see how we can make every card in a group have the same mod 4 result. For this explanation I will arbitrarily start with "group 3" (the physical last group) and ask the question "what must the suits be for each card in that group to make the mod 4 result equal 3".

With the card values in mind:
7, Q, 8, K, 10, 9, A, 3, 6, 5, J, 2, 4

The below is just a description of how this deck was created and may seem complicated, in actual practice the acaan calculations are much much simpler and I will explain later.

How the deck was created:
Let's start with the first card in "group 3" which is a seven (all groups in this stack start with seven) and ask what must it's suit be? in order for the seven plus it's suit value to mod 4 result to 3? Well our next target value above seven that will mod 4 to a result of three is the target value 11. Therefore how much must we add to the seven to get to 11? The answer is obviously 4. And 4 equates to diamonds. Therefore in the deck we are constructing group 3 (which is physically the last group) must start with the Seven of Diamonds.

The second card in "group 3" is a queen and to figure out its suit in order to mod 4 to a result of three we need to raise the value of 12 (Queen's value) to 15 which is an increment of three. Three equates to clubs, therefore the second card in "group 3" must be the Queen of Clubs.

The third card is an eight and to figure out its suit in order to mod 4 to a result of three we need to raise the value of 8 to 11 which is an increment of three which equates to clubs. Therefore the third card in "group 3" must be the eight of clubs.

I'll do one more just to illustrate the principle.
The fourth card is a king and to figure out its suit in order to mod 4 to a result of three we must raise its value from 13 to 15 which means two more notches up the ladder. Value 2 equates to hearts therefore the fourth card of "group 3" is the king of hearts.

I think you get the idea (using the appropriate suit for each card value to make it mod 4 to the same value as the other cards in that same group).

The next to last group of 13 cards I'm calling "group 2" which means all the cards in that group of 13 will have a mod 4 result of 2 (because I made sure that each card had the appropriate suit to make its value plus suit be 2 above the nearest multiple of four, note that the multiples of four that we will be concerned with are: 0, 4, 8, 12, 16)

The second group of 13 cards I'm calling "group 1" which means all the cards in that group of 13 cards will have a mod 4 result of 1 (because I made sure that each card had the appropriate suit to make its value plus suit be 1 above the nearest multiple of four).

The first group of 13 cards I'm calling "group 0" which means all the cards in that group of 13 cards will have a mod 4 result of 0 (because I made sure that each card had the appropriate suit to make its value plus suit be 4 above the nearest multiple of four which means the remainder when dividing by 4 will equal zero).

I have already done all the calculations and embedded them in to the following physical stack therefore at performance time your task is much simpler.

One more major element in the calculation is the FACTOR that is associated with the mod 4 result:

Result Factor
0 equals 0
1 equals 13
2 equals 26
3 equals 39

At performance time after a spectator names a card the mental calculation of the position of that card within the deck is quite quick:

Add the card value and it's suit and mod 4 that number thus you should know the above factor.

Then just add in the value of the named card's paired twin card. Easy peasy.

This uses the Harry Riser twins pairs technique.
The pairs pattern is mostly my own in order to have a good color mixture of suits and still meet the needs of a hidden 1 thru 13 arrangement.

Paired twins:
Ace and 7 (have a sharp angle at top)
2 and Queen (2 headed Queen)
3 and 8 (the 3 looks like half of an eight)
4 and King (the K and 4 have 4 corners)
5 and 10 (five and dime store)
6 and 9 (same symbol upside down)
Jack stands alone.

Card to position calculation Example:
A spectator names the two of clubs:
Magician or a shill mentally calculates:

2C
2 plus 3 equals five which mod 4's to 1.
Thus the factor is 13.
The paired value of a two is a queen which is 12.
13 + 12 = 25 thus the two of clubs is at position 25.

The reason I made the first 13 cards group 0 is so that the other three groups will have their mod 4 result numbers be the first digit of their factors. Example group 2 factor is 26. Group three factor is 39. Group 1 factor is 13. Group zero factor is zero. This makes the determination of the factor very quick and easy.

Note that if the mod 4 result is 0 then the position of the card is super simple it's just the value of the paired twin.

Seven Queens V1 acaan Stack:
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

To get the position of a named card:
Do a mod 4 on the card value plus it's SHCD suit value in order to get the 0 or 13 or 26 or 39 factor then add the paired twin card value.

https://www.themagiccafe.com/forums/view......forum=37

Click on the above link in secret sessions for more details.

In some of my other posts about the Seven Queens stack and the Jackknife stack I refer to the first physical group of 13 cards as being group 4 whereas in this post I refer to the first physical group of 13 cards as group zero because I have defined the mod 4 function here as simply being the remainder when dividing a number by 4.

The above fact only comes into play when the card's value plus it's suit equals 4 or 8 or 12 or 16. In those cases the FACTOR is zero.

I had run into computer functions that did modulus calculations that would never have zero as a result and would use the modulus number instead of zero if the modulus number divided into the target number an even number of times (zero remainder) and was thinking in those terms when I made the aforementioned posts.

In those other posts I should have defined mod 4 as simply being the remainder when dividing by 4 and allowing zero to be one of the possible remainders. This would eliminate having to use the term "group 4" in those other posts because "group 0" works perfectly as the name for the first physical group of 13 cards.

The above link into secret sessions is not working.

The below link should work:

https://www.themagiccafe.com/forums/view......forum=37

Above goes into secret sessions.

Next card SUIT new rules:
Instead of Napoleon battlefield using the NEXT card value and looking at prior card suit, just base the rules on the PRIOR card value and PRIOR card suit to get the next card suit (and use John F Kennedy White House for the next card suit memory methods).

This makes the calculation a little easier when doing a trick where the deck is cut and the magician glimpses the bottom card and needs to know what the top card is.

The results are exactly the same using this new method, it's just the new memory method for the next card suit is based entirely on the prior card value and suit in order to get the next card SUIT (the next card VALUE still uses the "Seven Queens ate ..." story memory method).

Next suit:

Forward one SHoCkeD:
3, 6, 10, J

Backward one SHoCkeD:
7, 8, K

Same color different shape:
A, 2, 4, 5

Exact same suit:
Q, 9

"Next card suit" White House memory methods:

10 days JFK (Jack) has Marilyn Monroe (36) as a guest at the White House and they go FORWARD for a walk SHoCkeD.

He has a 78-year-old King visitor who exits the White House by taking a BACKWARD step SHoCkeD.

There are young (1, 2, 4, 5 yr olds) visitors in line that each has a guest following them of the same color but different shape.

The Queen (Jacqueline Kennedy) is dressed to the nines but never changes her suit.

Note that this next card suit memory method is NOT used when doing the acaan trick, it is used when doing a trick where the deck is cut and the magician glimpses the bottom card and quickly mentally uses the "Seven Queens ate ..." to know the VALUE of the top card and the White House story to know the SUIT of the top card. It is also used when revealing a series of several cards that were dealt to spectators after the magician knows the value of one of the cards.


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

See The thread below for how to quickly calculate the top card when the bottom card is glimpsed by the magician:

https://www.themagiccafe.com/forums/view......orum=205

Note that this 13 stories method can also be used when revealing a series of six cards dealt.

Above thread is in shuffled not stirred.

This link shows how to do the difficult "card to number" calculation.

https://www.themagiccafe.com/forums/view......orum=205

It is in shuffled not stirred.

See the below on how to do "number to card" using the spectators fingers:

https://www.themagiccafe.com/forums/view......orum=205

Above link is in shuffled not stirred.

Quote: "I have posted more details to this under secret sessions and some info under shuffled not stirred but I wanted you math guys to have some visibility to this and perhaps you have knowledge of this mod 4 technique being used on a tetradistic stack before? Thanks."

A stack using that mod 4 technique is named a "Shadow stack."
The first shadow stack developed was Si Stebbins Pro by Dr. Solka, published in 2008. Looking at any card, you know the card's bank.
The idea and mathematics of a shadow stack were published in German and Austrian magic magazines Magie 01/2014, ALADIN 02/2014 and the eBook "Im Schattenreich der Spielkarten (In the shadow's realm of playing cards)', 2015, 48 A4-pages.

Other shadow stacks are, for example:
- After Eight Kings System by Mike Kettle & Dr. Solka, 2014
- Orbital Shadow stack by Mike Kettle & Dr. Solka, 2014, based on an idea of Peter Duffie and Lewis Jones
- Shadow Sequeira stack by Dr. Solka, 2018
- Shadow Quick stack 4.0 by Tawril/Dr. Solka, 2022 (private, not published); based on Quick stack 3.0 by Doug Dyment

Hcs, thanks so much for this information. I immediately purchased the $15 Si Stebbins Pro from lybrary.com just to see the differences and similarities to my Seven Queens stack. As you said the Si Stebbins Pro also uses the mod 4 technique to determine the offset.

In some areas the Seven Queens stack is easier and in other areas the Si Stebbins Pro is easier imo.

Later I plan to do a more detailed pro/con comparison (not revealing too much about the Si Stebbins Pro stack) and post it here.

Thanks again.
glowball

Note that hcs knows much of this so most of this post is addressed to the general members of the Café.

Comparison of the Seven Queens stack versus the Si Stebbins Pro stack:

First some definitions:
For brevity I'm using "7QS" to mean the Seven Queens stack and am using "SSPro" to mean Si Stebbins Pro stack.

The term "next card calculation" refers to the ability to know the next card in the stack when the card before it is known.

The term "acaan calculation" refers to the ability to know the exact position of a named card within the 52 positions.

Stack Comparisons:
The main difference is that the 7QS combines the Harry Riser pairs concept with the mod 4 concept thus supercharging the quickness of the acaan calculation. This is the only stack that I know of that combines these two concepts.

Another difference is that in the 7QS I moved the last bank of 13 cards to the top calling it bank zero. This helps a little bit to relate the mod 4 result to the offset number:
0=0
1=13
2=26
3=39
Notice that the mod 4 result number is exactly the same as the first digit of the offset number.
Thus the magician does not think in terms of banks, just what is the offset number and then add the Harry Riser pair number, simple.

Another minor difference is that the 7QS treats the kings like any other card (no exception rules).

When I developed the 7QS my entire focus was to create a very fast tetradistic acaan calculation stack that looked better than a traditional Si Stebbins stack and everything else was secondary. Therefore I had to sacrifice an easy "next card" calculation scheme by using the Harry Riser pairs concept. But this sped up the mental process of doing the acaan calculation.

My thought process was let's get the easiest and fastest "acaan calculation" and then later worry about how to do the "next card calculation" using mnemonic stories. So that's what I did.

SSPro:
To keep an easy "next card calculation" the SSPro has a modified version of the original Si Stebbins thus it is definitely faster and easier to calculate the "next card" (than 7QS) but to do this "next card calculation" SSPro could not use the Harry Riser pairs concept thus SSPro is a little slower at the "acaan calculation" imo. The whack-a-mole trade-off.

Because of the above facts SSPro causes the magician to have memorized the 13 positions of the cards within a bank and mentally separate the 13 cards into groups of four (I did not fully understand this however other magicians that use SSPro obviously do understand it).

The look of both stacks is superior to the standard Si Stebbins having suit color groups of one, two and three at a time however the SSPro maintains the increment by 3 on the value of each card (in order to keep the easy "next card" calculation). This could be detected by the spectators, but this is not a big issue imo. However the 7QS does NOT have a pattern within the 13 cards therefore I give the nod to 7QS as to the look of a face up spread of the deck.

An analogy:
When I was growing up in the 1950s and early '60s drag racing was really big and we would do things like get a lightweight Chevy II and put a 400 cubic inch engine in it. And it's main focus was to go a quarter mile very fast. The 7QS is like that ie: it was designed to mentally do the "acaan calculation" very fast.

The SSPro is like a 1980 Oldsmobile Cutlass that I used to own that was a very good all around car however it would not beat the above mentioned Chevy II in a drag race. The Chevy II was not as versatile as the Cutlass.

Getting back to the stacks:
In order to give the 7QS better "next card" determination I developed 13 little mnemonic stories so that now the 7QS can do the "next card" determination almost as fast as the SSPro stack.

Bottom line:
If a fast easy "acaan calculation" is primarily what you want then go with the 7QS.
If a fast easy "next card calculation" is primarily what you want then go with the SSPro.

Bear in mind that 7QS looks a little better than SSPro and note that you can also do a pretty good "next card" determination using the 7QS thirteen mnemonic stories.

Click on the below link and scroll down to the last post where it says:
"Here are more complete mnemonic stories"

https://themagiccafe.com/forums/viewtopi......orum=205

The above link is in shuffled not stirred.

Obviously these individual concepts are not mine, but I do claim originality to combining the mod 4 concept with the Harry Riser pairs concept together in the Seven Queens stack (at least until someone finds this written up in a old copy of Mum or Genie etc lol).

Your 7QS is wonderful.
Regarding "combining the mod 4 concept with the pair's concept together," I'm so sorry - no, see Shadow Sequeira Stack, 2015.

I immediately bought the Shadow Sequeira Stack from lybrary.com for about five dollars.
Wow, Shadow Sequeira is fantastic!

It and the Seven Queens stack are very similar and use the same algorithm to do the acaan calculation! I'm about ready to forget the Seven Queens stack and recommend to my magic friends to use the Shadow Sequeira (it's only five bucks) even though the Seven Queens stack is free.

There are some differences between these two stacks. The below are the pros and cons between the Seven Queens stack and the Shadow Sequeira stack (imo).

There is a difference between how these two stacks handle the Kings (this difference is very minor so I won't elaborate here, but I actually like the Shadow Sequeira method better even though it's an outlier method).

The "acaan calculation":
Both stacks use the mod 4 method to get the offset number (that has been explained further above in this thread so I won't elaborate on that). Both stacks use the named card's paired value to add to the offset number to give the final position of the named card, but the pairs they use are different so I will address that here:

The Seven Queens stack uses the Harry Riser type of pairs that are very visual to remember directly. Example: the three is paired with the eight (the "3" looks like half of an "8" so this is easy to trigger the magician's memory of this relationship). The "6" and the "9" are paired because they look like each other. Think of a two-headed queen (the "2" and the Queen are paired). These visual memory triggers are very direct.

Hans-Christian Solka (the inventor of the Shadow Sequeira stack) got permission from the Unknown Mentalist to use and publish the pairing scheme diagram used in the Karma stack based on a clock face which I will not elaborate on here. This is a very clever pairing scheme but may cause a half second delay in the mental calculation versus the more direct Harry Riser type of pairing method. When it comes to "ease of use" this difference in pairing methods of these two stacks is pretty minimal imo.

The "next card calculation":
This is where these two stacks differ considerably.

To calculate the value of the next card the Shadow Sequeira has a very easy to learn mathematical calculation with some minor exceptions. Going from a "6" to King to Jack is a rule breaker but easily memorized. The suit progression is done using CHaSeD (somewhat of an irony that the Shadow Sequeira uses SHoCkeD in its acaan mod 4 calculation but reverts to CHaSeD in the next card calculation but I think it had to be that way in order to keep the other features of the stack).

The Seven Queens stack does not use any mathematical calculation to determine the next card, instead it relies on its 13 mnemonic stories to determine the next card. Therefore when it comes to the issue of quickly learning the next card calculation the Shadow Sequeira is definitely superior to the Seven Queens stack.

Once the 13 stories are learned I believe at performance time the Seven Queens stack is a little easier to determine the next card because no math is necessary.

Random look of the two stacks:
Here is where the Shadow Sequeira falls down a little bit because:
It has a five or six value progression (except for the six, King, Jack) but this 5 or 6 value progression will probably never be detected by anyone.
The biggest problem imo with the Shadow Sequeira stack is that around the 4 kings there are three suits of the same color (a good thing) but everywhere else there is alternating suit colors.
By comparison the Seven Queens stack has none of the above issues, it looks very random within any 13 cards.

Note that any tetradistic stack can be detected if the audience is allowed to scrutinize the whole deck and compare the four 13 card groups. What I am talking about above is detectable patterns within a sequential dealing of cards. For example if the magician is doing an acaan trick using the Shadow Sequeira stack and dealing and counting cards face up on a pile on the table the audience may notice the suit colors alternating but when a king appears the alternating pattern ceases for three cards therefore the alternating pattern of the other cards is not a huge concern, but it is a concern.

Conclusions:
Six months ago if I had known about the Shadow Sequeira stack I probably would never have created the Seven Queens stack because the Shadow Sequeira Stack is so good and so cheap to own.

Speed of learning the two stacks:
If just learning the acaan calculations the two stacks are virtually identical in the speed of learning.

If learning the next card calculations the Shadow Sequeira stack is much faster.

Ease of performing the two stacks:
When doing an "acaan" trick I believe they're both about the same.

When doing a "next card" calculation I believe the Seven Queens' 13 stories method is less mentally taxing but the magician must stay in practice whereas the Shadow Sequeira mathematical approach is easier to remember (but take into account the Six, King. Jack anomaly).

The randomness look of the Seven Queens stack is definitely better.

None of the above pros and cons are a showstopper imo. A tough call as to a recommendation to my local magic friends that don't want to memorize 52 cards.

It just depends on which nuance a magician is concerned with.

Either stack is an excellent tetradistic acaan stack imo (mod 4 + pair rocks!) take your pick of either stack, you will be happy!

Thanks again to hcs for pointing out this excellent Shadow Sequeira stack!
glowball

Thank you for introducing the Shadow Sequeira stack. It's my pleasure, Glowball.
Thanks to Horatio Sequeira and The Unknown Mentalist for their basic and thought-provoking ideas.

I do not market my stacks since I rarely deal with card tricks. I have even shared some stacks (Si Stebbins 3/4, Si Solka, to mention some) only with friends. Those who are interested will find my stacks by necessity. Young magicians should learn a memdeck!

Mostly, I only write something when I notice little is known about a magic topic, or someone adorns with hawkish feathers.
Publications of some authors are very superficial and written or filmed under omission of historical development to make fast money. Their purchasers think their heroes invented sliced bread because of low knowledge!

The below link has the Seven Queens cheat sheet to do the Larsen and Wright type of three card suitability trick:

https://www.themagiccafe.com/forums/view......orum=205

This link is in shuffled not stirred.