Knowing what a single card is worth does not yet tell you how much you know at a given moment of the spot. The informative value is the share every element of the deck expresses by nature; what is needed now is the quantity each phase actually makes accessible.
That quantity does not depend on you. It depends on how many cards that phase has put on the table. What you then manage to do with it does depend on you: on your capacity to perceive, understand and interpret the information in front of you.
From informative value to the measurement of each phase
Once the quantity of information expressed by the single card has been established, the next step is to define the one generated by the combinations in the individual phases of the spot.
It is a universal value: it indicates how much information can be reached in a given phase regardless of the skill level of whoever is sitting at the table. It does not measure you, it measures the phase. And while the phase unfolds, that value influences everyone’s strategic choices in real time, each according to the skills they possess.
It is here that the potential use of specific skills is identified — the ones that, on their own, are not enough to guarantee they can be applied.
The magnitude that says which skills are needed
Since that information influences strategic choices, and with them the selection of the applicative skills of the parties involved, the magnitude takes the name of Informative Influence, the Ii.
The definition is this: the magnitude through which it is possible to identify the skills needed to face and beat your opponents. It does not tell you whether you will win the hand. It tells you which skills that phase puts at your disposal, and therefore which ones it makes sense to look for.
The name is not a coinage of the model. Informative influence is a concept from social psychology, from Deutsch and Gerard, 1955, and here it is applied to a specific context. Through the tools of qualitative analysis, to whoever best selects the information and the processes of signification related to it, the situation appears clearer.
Everyone sees the same information, and that is why the indices are constants
The contribution of the Ii is fundamental to the model, because it is in this condition that the qualitative difference between one player and another is generated.
All the actors involved in the spot have access to the same information. There is one board, the phases are the same for everybody, and the quantity each phase makes accessible does not change from person to person. It is precisely this feature that makes the indices constants: if the value were different for each player, there would be nothing to fix.
What changes is the quality of the choices, and from there whether the objectives of the spot are met. In the classic mode that difference turns out to be null, because the random component intrinsic to it cancels the difference before it can count.
The four phases change name because the question changes
Out of the elaboration of the indices comes a different way of naming the four stages of a spot, and the new names say what you do in each: at the pre-flop the classification of opponents, at the flop the semantic narrowing of the range, at the turn the definition of the situation, at the river the rectification or the confirmation.
At the pre-flop the information is scarce but sufficient to assess who has entered the action. Poker mathematicians use tables built on the relationship between the position you enter from and the equivalent combinations. With the change of paradigm those tables do not disappear: an imaginary card is added, on which you mentally group the characteristics of the opponents involved.
At the flop the difference between the two approaches becomes sharp. The mathematician asks how the flop has hit the opposing range, and on that calculates his own EV against the pot. Whoever applies the new paradigm is not interested in the pot, and the question he asks before any other is what that flop means for his opponents. At this point of the board the information acquired offers many interpretations of the situation, and the capacity to define it starts making the difference between competitors.
Recursive thinking, from level zero upwards
The elaborations of each phase develop over several levels of recursive thinking, with what the Treccani calls the matryoshka effect: every level contains the previous one.
At level zero there is the player who approaches the spot considering only the value of his own combination. At level one the one who considers his own and his opponent’s. At level two the one who also takes into account the value his opponent has attributed to his own, and so on, potentially to infinity.
At the turn the processes are the same as in the previous phases, with the complication of more information to process, and each player shows his own degree of definition of the very same situation. At the river you confirm what was determined at the turn, or you rectify it.
And it is at the river that a skilled player knocks down the random component: he understands that the value of his own combination is no longer the winning hand, and he preserves his stack and his stay in the tournament. The worldwide saying that «tournaments are won by folding» describes exactly this, without knowing it.
The more cards are known, the more information the phase makes accessible
The quantity a phase makes accessible is calculated by relating the informative value of one card to how many cards that phase has made known. The formula is Ii = Vi × Ec, where Ec is the number of known elements in the phase.
Which elements enter that count, phase by phase, follows from the logic of the completeness of information, and it is material to be seen on the seven cards every player comes to know.
On the result a clarification is needed, because it is easy to read it for what it is not. Saying that a given phase corresponds to a given percentage does not mean that you know that portion of the deck. It means that the structure of the board, the way the elements combine with each other and your pocket cards express that share of the total possible information contained in the deck: they are the informative opportunities those combinations are able to generate against the complete deck.
These values, on their own, are still not enough to enhance and preserve skills in a live tournament, and the dissertation demonstrates it step by step. The skills identified have to be verified in their applicability, and that verification goes through a second factor: the size of the stack you enter the spot with.