Philosophy, Technology and Math

This is Part I of my Head Games system of card playing. It is a system for card games using a standard deck of cards, yet played without an actual deck.  I am developing the system, and decided to present it now and see what others are doing and if I can get ideas for expanding what can be done with this.

Stated Simply
Is it possible to play cards without cards?  The answer is yes! I will show you how to work with a random deck of 52 cards, and give a way of selecting cards from that deck with any number of people playing.

I. Goal

To play various adventure games using a standard deck of cards yet having the deck of cards in your head only!

II. Defining the Deck and Mapping it to your Brain

The system of cards I am proposing is built around the following chart, which you will memorize easily, and which I will explain:

This chart is a system of mapping 52 cards to the numbers 00-51 such that picking a number from 00-51 will let you arrive at a card from a standard deck. I must explain the chart and how to use it, and with a little practice, you will be able to make good use of it as it will be stored in your brain.

Explaining the Chart
The chart has a header row on the top (in bold) that stands for the card (10, A, 2, 3, 4 …, K) and a side index-column for the suit (S, H, C, D) on the left, also in bold. Each entry in the table is a two digit number that identifies the suit and card. The first digit designates the suit. 0 = Spade (S) 1 = Heart (H) 2 = Club (C) 3 = Diamond (D)

The second digit designates the card number where a 0 = 10, 1 = Ace, 2 = 2, 3 = 3, … 9 = 9.

For example, 28 is eight of clubs (where clubs is suit #2).

This system works perfectly well for all the cards that are not face cards. That is, the numbers 00-39 map to all the cards, but don’t map to J, Q or K. That leaves 12 cards that don’t map well and in this way, the 12 face cards present a special challenge.

To that end, I decided to map the numbers 40 – 51 to the face cards. The first number can’t represent the suit, because it is only one number in most cases – the number four (40, 41, 42, 43…). My solution to that problem is to think of all the numbers 40 – 51 as the numbers 00 – 11.  It works this way:

40 -> 00
41 -> 01
42 -> 02
43 -> 03
44 -> 04
45 -> 05
46 -> 06
47 -> 07
48 -> 08
49 -> 09
50 -> 10
51 -> 11

In this way, if I picked card 48, I know I am dealing with a number greater than 39, which is a face card — so I have a conversion to do.  Namely, that conversion means 48 is now 08 (I’ll explain what to do with 08 in a moment).

Side Note Have you noticed that I often start counting at 0?  We are accustomed to counting starting at 1, but in playing cards in your head, 0 is always the starting point for all the charts and mapping.

Back to the issue of face cards.  Let’s assume we have 42 as the card we picked. 42 maps to 02 (as per the mapping given above where the 12 face cards go to 00 – 11.  In this case, the 2 stands for King and the leading 0 (zero) stands for Spades.

There are three face cards, Jack, Queen and King.  0, 1, 2.  However, for the sake of using your memory better, I picked 0 as going to Q since both symbols look like holes.   The number 2 maps to the King because it has two breaks coming off the main stem.  The Jack has one main vertical stroke in the letter J, so it maps to 1.  I did this as a memory aid, and it means that I convert 40, 41 and 42 to the Q of Spades, Jack of Spades and King of Spades, respectively since 40, 41 and 42 map to 00, 01 and 02 and.

I hope you follow me to this point.  If so, you will want to know about numbers higher than 42.

Let’s take 44 as a sample.  We know by now that 44 maps to 04.  Now we divide by 3. We have converted 44 to 04, now we divide 04 by 3.  The math works this way:  04/3 = 1 remainder 1 = 1r1 = 11.   I take the answer and the remainder and pack them together to get 11, and that gives suite = 1 (which is Hearts), card = 1. So 44 is 04 which is 11 which is Hearts, Jack.   Again, when we are dealing with face cards, the mappings are 0 = Q, 1 = J, 2 = K.

Let’s try some more.  If we randomly picked the number 48, the mapping is to 08 and then 8/3 = 2r2 => 22. And that means a  Clubs, King.   Given 49, we convert that to 09, and then convert that by 9/3 = 3r0 => 30, which is the 3rd suit, card 0 (where 0 maps to Q, and the 3rd suit is Diamonds). 50 goes to 10 and 10/3 = 3r1 = 31 and that is Jack of Diamonds. Finally, 51 goes to 11 and 11/3 = 3r2 => 32 and that is King of Diamonds (where the 2 is K and the 3 is Diamonds).

The first chart I presented above has a mapping of all 52 cards.  Now you can see why the face cards are in itallic.  They require that a special procedure be followed.

You must practice the system, and be good at dividing by three and knowing the remainders. If you can do that, you have a deck of cards in your head!

III. Choosing Cards

Having this mapping, I now have a system for picking cards. Two to many people pick a number between 00-51 at the same time. Then all announce their numbers for adding together. For example if the first person picks 32 and the second person picks 50 then the result is 82. That is the card picked. But that number is nowhere on our table, so we subtract 51 from it and get 31. Our card is 31. And 31 is Ace of Diamonds. The rule is this: Take any number of people and have each pick a number from 0 – 51; sum those numbers and then subtract 51 from that sum (as oft as you need) in order to get down between 0..51. That number is your card. Map it to a card using the table above.