Before quantifying how much information a player can acquire in a spot, what information is has to be defined. It is not a formal premise: everything else in the model depends on that definition.
The society we live in is often called the information society, and the reference is to the information-automation paradigm that characterises our era. The internet and the development of computer-mediated communication have imposed a new way of perceiving, understanding and interpreting reality: the theories of social action dominated by the a priori rationality of Weberian memory are abandoned for those of communication, for which social action is governed by the psychological need of human beings to enter into relation with others.
Information constitutes a basic dimension of reality, alongside those of mass and of energy, and it is not comprised in either of them. It is Anolli’s position, and the starting point.
Information is the perception of a difference
The first attempt at a definition of communication is Shannon and Weaver’s mathematical model of 1949, with their «Theory of information»: a linear transmission of coded information from a sender, through a channel, to a receiver who decodes it.
That model rests on a precise definition: information is the perception of a difference, Bateson’s formula, and Shannon understands it as a discrete quantity, observable and measurable. From that perspective information is not the datum in itself, but what passes from sender to receiver.
The definition the model needs, though, is another one, and it is Anolli’s: «information is the value of probability that is realised within many combinatorial possibilities (N choices) among H symbols».
It is this one that makes the indeterminability of information in poker understandable, made of the heterogeneity of the meanings each player can attribute to it. The mathematical model on its own does not explain the complex processes of communication, and leaves the task to the disciplines that deal with them: semiotics, the psychology and sociology of communication, the philosophy of languages, qualitative research methodologies. They are the same ones that find their application in the communicative dynamics of every spot of a live tournament.
Sklansky’s Fundamental Theorem, read in a structural key
That theoretical framework allows a theory the literature has always elaborated in a strategic key to be reformulated in a structural one: the Fundamental Theorem of Poker of David Sklansky, from 1987.
The principle says this: every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; every time you play it the same way, they lose. And it holds symmetrically the other way round, for what your opponents do with the cards of yours they cannot see.
Looked at from the structural perspective of the tournament rather than the strategic one, the theorem highlights, in a wholly implicit manner, the importance of a deep knowledge of information in order to succeed in the empirical phase. Sklansky’s work then unfolds into the elaboration of mathematical concepts and of the strategies that follow from them, with no reference to the scientific disciplines of communication.
Two premises: the primacy of the deck and the conduct
The theorem serves the model because it provides two basic premises. The first assigns informational primacy to the individual components of the deck of cards on which the entire spot develops. The second highlights the need to pair the knowledge of information with a conduct of the decision-making processes consistent with the strategies for success.
The second is a theme deeply felt in the community, and it has a name borrowed from pinball: tilt, the condition in which the emotional state takes over from rationality and leads to a style of play far from the optimal expected value. Every poker theorist deals with it, and they all insist on the importance of a disciplined conduct to protect one’s results.
Completeness is reached only if all the phases are revealed
From those two premises comes the Theory of Completeness of Information in poker, the TCI: complete knowledge of the information and the identification of the skills connected to it can be reached if, and only if, all the phases of the spot are revealed. It is an absolute truth no player can escape.
Perfect knowledge of the relation between your combination and your opponent’s, and of both against the board, acquired phase by phase, can determine the exact value of your hand against those same opponents. In other words: the more knowledge you have of your opponents, the closer and more consistent the literal interpretation of Sklansky’s theorem becomes.
And it is here that the TCI also says how skill is measured. It is measurable by the degree of individual quality of the single subject involved in the capacity to perceive, understand, interpret and elaborate the information matured over the course of the spot, in relation to the final outcome.
One hundred per cent of the information is in the whole deck
According to the logic of completeness, every player can obtain one hundred per cent of the available information if, and only if, the river is reached, when all the components of the deck are revealed.
Although it is true that only up to the river can you receive all the information about the spot, by the informational primacy of the individual elements one hundred per cent of the information is contained in the whole deck of fifty-two cards. Completeness therefore takes into account the invisible arrangement of all the components too: depending on how chance has laid them out, they influence the combinations of the players’ pocket cards and the texture of the board, that is, the way the elements arrange themselves along it.
If after the initial deal you had the chance to see all fifty-two elements of the deck, you would really have one hundred per cent of the information available, and you could potentially identify one hundred per cent of the skills in your possession, activating at the same time the development of new ones, up to pseudo predictive skills: defining the board before it is even revealed. It would decidedly be a great advantage.
Seven cards out of fifty-two
In reality you gain progressive access to only the five elements of the board plus your two pocket cards: seven cards out of fifty-two. Of all the information contained in the deck you can know only a portion.
Hence the next step: understanding the informational influence of the known elements, which develops progressively across the single phases in the form of a quantity of information potentially accessible for each phase of the spot. The term is not a coinage of the model: it comes from Deutsch and Gerard, 1955.
The tool that allows «the value of probability that is realised within many combinatorial possibilities» to be defined at every phase comes from semiotics and the philosophy of languages, and it is the principles of componential semantics. It is from there that the indices draw their values, and therefore also the distribution of the pot in the all-in phases.
The values that come out of it, however, are not enough on their own to enhance and preserve skills in a live tournament: the applicability of the skills identified has to be verified through the size of the stack. It is the step with which the dissertation closes the argument.