Measuring skill in poker sounds like an overreach. And yet, once you have established what information is and reread the fundamental theorem in structural terms, the step becomes possible. The study takes it by formulating the Theory of Information Completeness: not a calculation technique, but the conceptual instrument that establishes the condition under which a player really holds everything there is to know.
- What a skill actually depends on
- The Theory of Information Completeness
- What you know when you know everything
- Why skill becomes measurable
- The condition: reaching the river
What a skill actually depends on
Before you can calculate a skill index you need to know what that skill depends on. The study identifies two factors.
The first is the quality of the information acquired in the various phases of the spot. The second is the player’s capacity to perceive, understand, process and interpret that information, translating it into the best strategies for eliminating opponents and taking their stacks.
They are two distinct things, and it is worth keeping them apart: the first concerns what the table makes available, the second what the individual player manages to do with it.
Further on the study reaches a tighter formulation: skills depend on two distinct but deeply interdependent factors — the information acquired and the size of the stack.
Acquiring information progressively through the spot allows the useful strategies to be identified; the size of the stack measures how far those identified skills can actually be applied. The second of the two is a subject of its own, addressed when discussing chip utility.
The Theory of Information Completeness
From the rereading of the fundamental theorem of poker and from the two premises that follow from it, the study formulates a new theory: the Theory of Information Completeness in poker.
The statement is a condition, and the constraint it sets is a strong one: complete knowledge of the information, and the identification of the skills connected to it, is accessible if and only if all the phases of the spot have been revealed.
The “if and only if” is not a figure of speech. It is not enough for the revealed phases to be many, or almost all: either they are all revealed, or knowledge is not complete and the connected skills remain partly unidentifiable.
The study calls it an absolute truth no player can escape. It does not depend on the level, experience or clarity of whoever sits at the table: it depends on the structure of the hand itself.
What you know when you know everything
It is worth clarifying which knowledge is being talked about, because it is not knowledge of everything that happens at the table.
It is perfect knowledge of a precise set of relations: that of your own combination against the opponent’s, and that of both combinations against the board, acquired across all the phases of the spot. Once you hold them, it becomes possible to determine the exact value of your own hand against those opponents.
From this follows a corollary that closes the circle with the previous article: the more knowledge you have about your opponents, the closer and more coherent the literal interpretation of the fundamental theorem of poker becomes.
Why skill becomes measurable
A distinction is needed here, because the word “measurable” has already appeared in this series with a different subject. In discussing what information is we saw that it is information that is a measurable quantity. Now the subject changes: it is skill.
Skill is measurable by the degree of individual quality of each player in perceiving, understanding, interpreting and processing the information matured during the spot, in relation to the final outcome.
And here lies the reason such a measure makes sense. All the players involved in a spot have access to the same information: no one has more of it. This makes the skill indices constants, identical for anyone sitting at the table, and shifts the difference in the final result entirely onto the quality of the individual skills.
It is the step that makes measuring skill in poker possible: no longer the judgement “they played well”, but the ratio between what was knowable in that hand and how much the player managed to recognise and use.
The condition: reaching the river
From the logic of completeness follows an operational condition, the most concrete point of the whole argument: every player can obtain 100% of the available information if, and only if, the hand reaches the river with all the components of the deck revealed.
Put differently: a hand that closes before the river delivers complete information to no one, and therefore does not allow the skills that were in play to be identified in full.
It is a demanding condition, and it is the theoretical root of a problem addressed elsewhere: making a hand reach the river often enough for skill to emerge. The way the model intervenes on this point is discussed when dealing with variance in poker.
In the next article we will see how this theory applies to a real spot, phase by phase, and how the information actually available comes to be quantified.
