“There is nothing so terrible as activity without insight.”
– Johann Wolfgang von Goethe

There’s no escaping it- from a purely financial standpoint poker is a negative sum game. This simple fact presents a conundrum that every mainstream poker training business tries very hard to ignore: It is impossible to have as a sincere mission the objective to ‘teach the world to play great poker’.

“Teach the world to play great poker” – the reader may laugh at loud at the very idea of it. Yet the absurdity of this phrase belies the seriousness of a structural problem that pervades the poker training industry: There is an inevitable conflict of interest that arises between expanding the customer base of a training site and the benefit derived from that training site by each individual customer. In this way, the very success of a poker training site punishes its customers!

In this article I am going to introduce a metastrategic concept that is essential to the success of your poker career- the value of strategic information. After reading the article you will understand why so many players resent mainstream poker training sites for cannibalizing the games, and how to estimate the value of emerging opportunities in poker. You will also discover why a different approach to strategic information distinguishes Cardquant from mainstream poker training sites.

Of necessity this article will only appeal to a fraction of my readership, but those are the very people that I am most eager to make a connection with. So if you really enjoy this article, and want to see the next article in the series come along shortly, please take the time to introduce yourself in the comments. Let’s get started…

This article is the first in the Cardquant Identity Series– a series in which I will introduce a number of new concepts to my readership, explain how they relate to my work at Cardquant, and how my work at Cardquant relates to my larger vision for my scientific research and my philosophical writing.

Information Distribution Curves

It is well established that poker games are games of incomplete information. What is seldom explicitly stated, much less formalized, is that each variant of poker has its own associated information distribution among the competing population, and that this distribution has a strong deterministic influence on the distribution of profits from that game variant.

I have developed the ‘Information Distribution Curve’ as a visual way to represent the various structural features that determine the value of information in a game variant.

Let’s take a look at an example of an Information distribution curve for a poker variant in order to familiarize the reader with the key features of such curves.

Poker Information Distribution Curve

The curve shown ranks the population in order of the level of strategic information about the game that they retain at a given moment in time. The ‘x’ axis spans the population, terminating at the 100th percentile. The ‘y’ axis indicates the quantity of information that each player retains, as a fraction of the theoretical perfect strategic understanding. Whether this perfect understanding is attainable, or is in fact some form of infinity for any given variant, is a philosophical digression that is not significant for the discussion at hand.

I have marked out three key points on this curve:

  • Imax :- This indicates the participant who has the highest level of strategic information for the game variant.
  • Ihero:- This point represents you, the hero, indicating your current level of strategic information for a game variant in the context of the wider population.
  • Iopp:- This point indicates the level of strategic information for a single opponent on the curve. Any point on the curve which is not you represents a potential opponent.

The double-headed blue arrow indicates ∆I: the difference in information level between you and a given opponent, with a positive value giving you the advantage and a negative value conferring an advantage to your opponent. In a heads-up game, only one ∆I would be relevant but in a 6-handed cash game, or a multiplayer tournament, the level of strategic information for every one of your opponents in the game matters (although each opponent’s level is not equally weighted- another complication).

The information landscape for any given game variant will develop over time. Each single-headed arrow on the curve indicates a feature that will change across time:

  • The black vertical arrow adjacent to Imax indicates the rate of discovery dImax/dt of strategic information at the leading edge of the game variant.
  • The black vertical arrow adjacent to Ihero indicates the rate dIhero/dt at which you, the hero, learns new strategic information. That similar such arrows could be drawn for every one of your opponents follows trivially.
  • The white horizontal arrow on the curve indicates the ‘information drift’, which is a term I have coined to describe the rate at which the high level information accessible to those at the top of the population flows to those lower down in the population. For now a qualitative description will suffice, although there are some natural ways to formalize information drift which I will briefly discuss below.

Before we continue there is one other essential feature common to all game variants that I have not indicated on the diagram above- the information ceiling. The information ceiling is the theoretical limit to which it is possible to formalize any particular game variant. The reason that tic-tac-toe is not played for money, and in fact rarely even played at all