The deck of cards as an alphabet is not a literary image: it is the technical step by which the study arrives at a measurement. A card on its own says very little — exactly like a letter. And like a letter, it acquires sense only by combining with the others. From here comes the minimal unit of information in poker, and a number for it.
- The smallest unit of the deck
- An alphabet of fifty-two letters
- What a single card says on its own
- The information value of one element
- The formula, and where it leads
The smallest unit of the deck
In the previous article we saw why the code of poker can be broken down: it meets both conditions a linguistic model requires. What remains is to carry out the decomposition itself.
In the specific case of Texas Hold’em, and in the light of the fundamental theorem of poker, the task is to define the smallest quantity of information expressible by the smallest constituent unit of the fifty-two card deck: one that cannot be broken down further. The study calls it the Information Unit, Ui for short.
It is a less abstract step than it sounds: it simply means breaking the deck down into its minimal constituent parts, that is, into the single element. It is the equivalent of what Hjelmslev, in 1943, defines as the phoneme in linguistics: the minimal unit below which one does not go.
An alphabet of fifty-two letters
An element taken on its own offers a rather limited value of information, confined to its own nature. This is where the analogy becomes useful: every elementary component of the deck can be considered a letter in an alphabet of fifty-two letters.
Take the letter A — though the reasoning holds for any letter. On its own it expresses the basic information that concerns it by nature: it is the first letter of the alphabet, it is a vowel. Little else.
What it cannot do, on its own, is express a complete idea. It needs to combine with the other letters in order to give rise to meanings, that is, to information. Nobody writes a word with a single letter.
What a single card says on its own
For the deck of cards it works in exactly the same way. Each element on its own, not further decomposable, emits a limited quantity of information of its own: what constitutes it.
Which information? The value that card holds within the deck, its position in it, the symbols printed on it. Few things, all intrinsic: none says anything about how the hand will go.
To generate the combinations that are useful to the development of a spot, that card needs to combine with the other components of the deck. On its own it remains a letter.
The information value of one element
The next step is to quantify that little. It means assigning the information unit an Information Value, Vi for short, defined as the potentially expressible quantitative capacity of information of each single element present within the deck.
Here the study warns against a misunderstanding: this is not a low value. The reason is that it does not measure the card in isolation, but refers to the many informational opportunities that the combinations of the known cards are able to generate with respect to the complete deck.
To calculate it, one returns to the definition of information established at the beginning of this path: the probability value realised within many combinatorial possibilities. It is that definition, and no other, that makes the calculation possible.
The formula, and where it leads
The information value is expressed like this: Vi = Ic / (Ui × M).
Ic corresponds to the total information contained in the deck, expressed as a percentage in line with the probability value of the reference definition: it is 100%. Ui corresponds to the single component of the deck. M is the deck of cards, which counts fifty-two elements.
Once the calculation is done — one hundred divided by fifty-two — the information value of the single unit comes out at 1.92% of the total information transmitted by all the components of the deck. It is the portion each single element can express, and to which access is potentially possible.
With this, the path closes where it began. At the outset we established that information, in poker, is a quantity and not a feeling. Here that quantity has a unit of measurement — the single card of the deck — and a number. What remains is to see how those units come into play: the four stages of the hand do not reveal the same amount of them, and do not ask the same work of the player.
