This thread shows how to eliminate the bothersome -5+5 part of the Harding stack calculation. This is done by having a special card that is openly shown to the spectator and audience that has the permissible card choices (for doing card to number) on one side and the permissible number choices (If later doing number to card) on the other side of that special card.

Below is based on imaginary position in Ace thru King of CHSD deck then flip the 2 digits.
Below lowercase suits indicate cards that need -5+5:
10C, 7H, 4S, AD, JD, 6c, 7c, 9s, 6d, AC, JC, 8H, 5S, 2D, QD, 3h, Kh, 10s, 7d, 2C, QC, 9H, 6S, 3D, KD, 4h, As, Js, 8d, 3C, KC, 10H, 7S, 4D, 8c, 5h, 2s, Qs, 9d, 4C, AH, JH, 8S, 5D, 9c, 6h, 3s, Ks, 10d, 5C, 2H, QH

CARD NAME TO NUMBER:
The permissible cards a spectator can choose from are permanently written hodgepodge on a blank card ahead of time. During performance The magician shows this card to a spectator and asks them to name anyone of these cards:

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

You could also have the same cards written a second time directly underneath the above list to make it look like it's a full 52 cards on the hodgepodge list.

This technique eliminates the possibility of having to do the -5+5 because those 22 card names are not on the list.

Of course you use the normal Harding stack calculation of determining where in the imaginary spread the named card resides and then flip the two digits. If the card resides at a position less than 10 then imagine a zero in front of that position then flip the two digit number.

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NUMBER TO CARD:
On the other side of this special blank card have written the permissible numbers that the spectator can choose:

1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 50, 51, 52

Write the above numbers in hodgepodge fashion and you could write them twice to make it appear as though there are 52 numbers but instruct the spectator to name out loud one of the numbers on the card.

This technique eliminates the possibility of having to do the -5+5 because those 22 numbers are not on the list.

Of course use the normal Harding stack calculation of flipping the named number and then determine what card resides in that imaginary position. Note if the named number is less than 10 then imagine a zero in front of that number before you flip it.

Hi Glowball,

It is not clear to me what this is really supposed to achieve.

The purpose of the Harding system, as I understand it, is to create a stack in which the performer can "easily" know the position of every card. I.e. it is an alternative to a memorised deck, based on a formula instead. This means it can be used in many situations. Therefore - I think this is generally accepted - the formula must cover every card/position. Which it does.

You seem to be describing a "solution" in which the spectator is limited to choosing a subset of cards/numbers. This may be acceptable in some situations, but not in most, given what I said above. You haven't actually specified what effect you might use the above approach in. Perhaps if you described a whole effect it would make more sense (to me).


Also, for what it's worth, I think there is (for me, anyway) a fundamental problem with the Harding approach. It is predicated on the assumption that you already know the position of every card in NDO. I certainly don't; I need to calculate them (albeit the calculations are fairly simple). So - for me - Harding is not an "easy" stack after all. Personally I think it is better to memorise a stack.

BUT here is an interesting idea. If you already know one stack (eg Mnemonica) you could use Harding to generate a second "virtual" stack. In this case you start from a situation where you DO already know all the card stack numbers. Ironically this will not work for my own stack, which is based ion Joyal's so uses certain mathematical principles. However I think it should work for any random stack; and also I think for Tetradistic stacks.

Regards
Nick

I can only agree with Nikodemus' evaluation of the Harding Stack; in addition to the major flaw he describes, the stack is also inconsistent in its rules (there are exceptions that must be simply memorized) and exhibits several repeated patterns. Although notable in its day (1962), it has been surpassed by improved designs.

The Harding Stack did introduce the notion of transforming identities from one stack to another, an idea that remains useful. In fact, it propels my own Q Stack (although I use it in a different fashion), which is 100% consistent in its algorithm (no exceptions to the two simple rules for converting between cards and positions) and presents as truly random.

Click here to view attached image.

I think I'll call this special card the Midas Card.

As usual Nikodemus has raised some excellent points and asked me to give an example of what this midas card accomplishes so here goes:

First some background: I have been looking for a calculator/formula deck to do acaan (especially card to number not so much number to card). This stack would be primarily for magicians that are NOT deep into card magic to use and get nearly the same audience reaction as the same trick done with a mem deck.

There are a lot of good calculator stacks out there but I wanted something that was even quicker to learn so have created several stacks of my own but the traditional Harding stack may be even better when coupled with my Midas card.

The key features of my ideal hobbyist acaan stack/deck are:
1. good random look
2. quick to learn formula
3. easy to perform
4. spectator has some choice of card (but not necessarily any card)
5. quick to train a shill

The above was my original criteria but since I discovered that Aronson and others have a simple solution to criteria number 5 above so we can scratch that criteria off because all stacks can use the instant shill method (I like to use a simple minus eight).

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

So now my ideal hobbyist acaan stack/deck criteria are:
1. good random look
2. quick to learn formula
3. easy to perform and preferably no equivoques
4. spectator has some choice of card (but not necessarily "any card")

The Harding Stack scores very high on criteria one and four but is a little more difficult on criteria two and three but some magicians have successfully used the traditional CHaSeD based Harding stack for years so the calculations are not too difficult.

The hobbyist magician might not be inclined to use the excellent looking Harding stack because of the special calculations but I thought that using the Midas card would greatly simplify the calculations (not only does it get rid of the -5+5 the Midas card also gets rid of the special rule for position number six and seven).

As to knowing where the named card is in the imaginary spread It has always been very easy to calculate: use the card value then
If hearts add 13
If spades add 26
If diamonds add 39
Note for clubs that are lower than 10 you mentally supply a leading zero ie: 5 is 05.
Next flip the two digits in the result.

That's it when used in conjunction with the Midas card (no -5+5 nor consideration for position 6 or 7).

OK let's get to the presentation of how this could work:

Ahead of time the magician secretly tells a spectator (magician's instant shill) to subtract 8 from last suggested number.

Presentation:
Magician presents a deck of cards still in its case.

Magician shows the Midas card to a spectator and says "Often times when I ask a spectator to name a card they will say ace of spades or queen of hearts and then that kind of takes away from the effect that I'm about to do therefore to prevent any prejudicial thoughts I want you to randomly touch any card name on this list of 52 cards and then loudly tell everyone the card you have touched".

Let's say they touched 6S.
The magician says "do you want to change your mind and touch another card name or do you want to stick with the six of spades?"

Let's say they stick with the six of spades.

Magician mentally adds 26 to 6 and gets 32 then flips those two digits giving 23.

So the magician knows the six of spades is at position 23. Very simple. To know what number to suggest to the shill the magician mentally adds 8.

The magician turns to the shill (the audience thinks the shill is a random spectator) and says "I want you to name a number from 1 to 52 like 12 or 31 but not those numbers, think of your own number and say it out loud".

The last number the shill hears is 31 therefore the shill mentally subtracts 8 and says "oh, how about 23".

The magician picks up the card case gives it a shake and says "I have now magically moved the eight of spades to position 23".

The magician hands the deck to a spectator and tells them to hold the deck face down and deal the cards face up to position 23 and It is the six of spades!

With the use of a Midas card the normal CHaSeD based Harding stack is also very strong on criteria 2 and 3 below:
1. good random look
2. quick to learn formula
3. easy to perform and preferably no equivoques
4. spectator has some choice of card (but not necessarily "any card")

I think this would be great for a hobbyist magician that does not want to memorize a whole deck.

For me personally I have memorized the Aronson stack and used it for many years and will continue to do so therefore I have no need of a Midas card but others may find the use of a Midas card beneficial.

Thanks to Nikodemus and ddyment for your comments.

On a trip together about 20 years ago or so Stephen Bargetze convinced me to learn the Aronson stack. Thanks, Stephen.

Oops, I wrongly said:
"I have now magically moved the eight of spades to position 23".

Instead of eight of spades it is of course the six of spades in our example.

The Harding stack has for sure his limits, that can be major issues or not depending on the person and the application.

However it has some extra features still unsurpassed in my opinion (e.g. absent in the Q-stack):

- easy setup from and to NDO
- easy calculation of next and previous card

There is a modified Harding stack that is a little better as well (at least for me).