Knowing which skills a phase makes available is not yet enough. Informative influence tells you which skills you could use in that phase; it does not tell you whether you are in a condition to use them.
That condition is the stack. It is the second of the two factors the indices depend on, and it regulates how much of what you have identified you can actually put on the table.
The skills you have identified are not yet the ones you can use
It is the size of the stack that determines the empirical application of the skills identified in the analysis of the information acquired. However skilled you may be, nothing will be possible if the stack you hold is not sufficient to support the action you have identified.
Between recognising the skills and being able to apply them there is therefore a step that is not automatic, and that is what this second factor measures. It happens systematically: you have the best tactical competence and you find yourself unable to practise it, because the chips do not support the action you had in mind.
It is a factor in its own right, not a consequence of knowledge. No amount of analysis compensates for it.
The measure of a stack is not how many chips you hold, but how many skills it supports
The concept needed here is not the absolute size of the stack. It is chip utility: the competitiveness of your stack against those of your opponents, in a grid that classifies every stack according to its own size.
The value of that utility is directly proportional to the skills you are able to express. It does not measure wealth, it measures practicability: it says which actions that pile of chips still leaves open to you, and which ones it has already closed.
It is a change of question. Not «how much do I have», but «what can I still do with what I have, sitting at this table, against these opponents».
Acquiring utility means subtracting it from your opponent
The concept rests on a corollary worth reading twice: the moment you acquire utility, you subtract it from your opponent, and vice versa. It is not a quantity each player cultivates on his own. It is a quantity that moves from one stack to another.
From this follows, for every player, the need to keep his own chip utility as high as possible by trying to subtract it from his opponents. And here the circle closes with the second change of paradigm the dissertation proposes for live tournaments: setting your strategies no longer by virtue of the pots, as is necessary in cash game, but in relation to acquiring your opponent’s stack and consequently eliminating him.
It is the same principle that governs the distribution, seen from the other end: there you measure how much skill a phase still contained, here you measure how much of it you can actually spend.
Snyder arrives at communication without naming it
The author chip utility comes from is Arnold Snyder, and he is controversial for two reasons. The first is that he was the only one to develop strategies founded exclusively on the structure of the tournament — the progressive increase of the blind levels — and specifically for live tournaments. The second is that he was the first to announce the ineffectiveness of statistical calculation in live tournaments, proving wrong some mathematical theories that had been applied to them.
There is a third aspect, though, and it is the one that makes him useful to this model. Snyder uses mathematics to express his concepts, but the theories he presents are founded on the paradigm of communication and on the tools it offers. Like Sklansky, he never expressly cites any of those disciplines; reading his works you cannot help noticing them.
The point where this is most explicit is emotional intelligence. The process of signification we have talked about is condensed by Snyder into empathy: the capacity to understand other people’s emotions and to perceive and interpret the sensations produced over the course of the spot. It is an aspect that counts, because it highlights the substantial difference between the live tournament and the online one.
Sixty per cent becomes a parameter of the model
The study of chip utility serves to define the minimum stack needed to face every phase of the spot without being forced to go all-in before the river. Snyder calls that condition competitive utility, and sets it at a minimum of sixty big blinds, equal to a utility of sixty per cent.
Below that threshold the arithmetic does not work: an action built on conquering your opponent’s stack inevitably leads to committing every chip well before the river, and in the all-in condition every piece of information, every choice, every skill is cancelled. It is the same ground the bad beat grows from.
Snyder himself warns that no simple way of calculating utility exists, because much depends on the real qualities of the individual player, and he often repeats that a poker tournament rests more on emotions and perceptions than on numbers. Having taken note of that limit, the dissertation adopts the sixty per cent utility as the minimum basis for its calculation all the same, because a uniform value across every phase is needed to guarantee command of the skills up to the final execution of the spot.
The stack is all there from the start, the information is not
Between the two magnitudes the indices are built on there is a difference that decides the shape of the calculation.
The informative units present themselves gradually over the course of the spot: at the pre-flop you know two cards, at the river many more, and the quantity of accessible information grows phase after phase. The chips do not. The chips available to each player are always available in the same way over the course of the hand.
The stack will tend to decrease during the action, which is obvious. But the initial strategies are elaborated on the basis of the one you entered the spot with, and you carry that value with you into every phase.
This is why the magnitude that derives from it — the influence of the stack, the Is — does not vary from one phase to another: it stays fixed at the sixty per cent of competitive utility from the pre-flop to the river, while informative influence grows. One constant and one variable, and it is on these two that the dissertation builds the calculation of the indices phase by phase.