Complicated Indifference

My latest poker strategy article, Complicated Indifference, is now appearing the March 2018 issue of Two Plus Two Magazine. It aims to explain the value of acquiring at least a low level understanding of game theory, even if you know that your opponents will make plenty of exploitable mistakes:

Many poker players are introduced to game theoretical concepts like balance and indifference in the form of a simple example in which one player holds a bluff-catcher and faces a bet from a polarized range. These players tend to understand that there is some sort of theoretically optimal ratio of bluffs to value bets for the betting player, even if they don’t fully appreciate what it is, where it comes from, or why it matters. Likewise, they understand that there exists some optimal calling frequency for the bluff-catching player, though they may not know exactly how to calculate it.

Though not technically wrong, this simple example misrepresents the complexity of the real life situations that arise much more frequently. In fact, most ranges aren’t perfectly polarized, at least not at equilibrium. That is, in the majority of real no-limit hold ‘em situations, there are good game theoretical reasons to bet a variety of types of hands, many of which will not slot into neat categories of “bluff” and “value bet”.

It is in these more complex situations where understanding the game theory behind poker is most valuable. So, while it’s a good starting point to learn the game theory of a simple situation such as the one above, it’s not hard to see why players who understand only this situation fail to see the utility of game theoretical approaches. This article will consider, in broad strokes, the game theory underlying more complex bluffing and bluff-catching scenarios. While it is admittedly not practical (and often not desirable) to memorize and implement perfectly balanced mixed strategies, understanding the basic theory behind these strategies is quite useful for crafting exploitive strategies.