What would happen if you folded every time you had a weak hand and an opponent bet into you? Any moderately attentive opponent would notice this trait and bet into you mercilessly irrespective of their holding. You would constantly get bluffed off your equity and spew chips as a result.
How about calling every bet you faced with a range of hands that included absolute garbage? That would also be a massive leak. Opponents will mark you as a calling station and value bet you into oblivion.
There clearly needs to be some middle ground where you defend against bets with an appropriate frequency. But how does one determine that frequency? On what factors does it depend? Getting our defense frequency right is essentially knowing how to defend ourselves in poker, since savvy players will take advantage of our mistakes to win our chips.
Poker players often look for silver bullets that allow them to simplify their decisions. The problem with this approach is that any poker recipe of the form “if X, do Y” is invariably an oversimplification. Fundamentally, poker has too many variables such as board texture, bet size, positional formation and others, to make such cookie-cutter prescriptions viable.
In the case of defending against bets, one algorithmic attempt to determine the appropriate frequency is the MDF or Minimum Defense Frequency. You may have also heard MDF referred to as “one minus alpha.” Here are the relevant formulae for those of you who like this sort of thing:
To appreciate the relevance of these expressions, let us start with alpha. From the point of view of the bettor, this represents the minimum folding frequency of their opponent that generates automatic profit. In other words, if the defender folds more often than this, they will be auto-exploited by the bet. The bettor, in this sense, always wins, irrespective of the cards they hold.
This leads directly to the idea of minimum defense frequency. In order to avoid being auto-exploited by the bettor, the defender needs to continue at a frequency that satisfies the MDF.
So far, so good. Allowing our opponent to auto-exploit us sounds like a bad idea, but now we have a nice, tidy formula to calculate our continuing frequency that prevents such exploitation. From this frequency, we can construct a continuance range.
Unfortunately, there is a problem with this line of reasoning that can be illustrated by a simple thought experiment. Suppose on the river our opponent bets all in for $100 into a pot of $100. The formula for the minimum defense frequency tells us we must call 50% of the time to avoid our opponent showing an automatic profit.
But what if this particular opponent only pots the river with the stone cold nuts? Calling with half our range would be completely bonkers, right?
This might seem like an unrealistic example, but it does shine an important light on the whole philosophy behind MDF. For one thing, it tacitly assumes that our opponent is bluffing at a frequency that is well-motivated by theory.
When we have information on our opponent, we will often have good reason to deviate from MDF, but what if we are playing against a complete unknown? Should we apply MDF in such situations?
You may have read that against unknowns, MDF is particularly applicable because it is a GTO concept. In reality, MDF is not a GTO result at all. Here is coach w34z3l to address the origin of that misconception, and to explain why MDF leads to quite different defending frequencies than those recommended by GTO solvers.
As w34z3l demonstrates using solutions from GTO+, the defending frequencies in certain situations determined by GTO can deviate significantly from those given by MDF. This puzzles many players because both MDF and GTO are, in some sense, strategies that stem from the imperative of avoiding exploitation.
The reconciliation of MDF and GTO arises when one realizes that it is okay (and in fact GTO-approved) for the aggressor to generate automatic profit from their bluffs. It is not correct, as MDF assumes, for the defender to make the aggressor’s bluffs 0EV. The correct objective is to construct our defense such that our opponent’s bluff range is indifferent between betting and checking.
The primary takeaway from this discussion is that MDF provides a useful baseline in many situations, but if used blindly it can be extremely dangerous. Moreover, attempting to use MDF as a basis for range construction should be avoided. Indeed, if one begins with a solid strategy based on GTO or population exploits, our defending frequencies have a happy tendency to take care of themselves.
A key result from the above discussion is that our position matters when constructing defense ranges. Generally, we should defend less when out of position to our opponent than when we are in position.
This should comes as no surprise if you are familiar with the importance of position in poker, as emphasized in many different contexts in our training material. Equity realization is simply more difficult when our opponent has position on us, thus we need a tighter continuance range when suffering the positional disadvantage. It also illustrates an intrinsic weakness of the MDF, which makes no reference to position.
It turns out that this general argument can be extended by another step. It is not just position that impacts our continuance strategy in a given hand of poker; formation is also a key consideration. For example, when we open raise from UTG and get called by CO or we open from CO and get called by BTN, we are OOP in both cases. However, because preflop opening and calling ranges are different in the two cases, the subsequent streets play quite differently. This illustrates another nuance in correct defending frequencies.
Here is coach w34z3l to take a closer look at the relevance of formation in poker strategy.
Now you have a better handle on the importance of formation in poker, it is important to appreciate that many of your opponents may ignore this critical concept. As usual, this is particularly the case at lower stakes. This has a couple of consequences as you try to dominate such players.
First, an ignorance of formation invariably means that even a somewhat studied player will make frequency errors. For example, if your opponent uses identical c-bet frequencies irrespective of formation, their frequencies will deviate from theory in most formations. Consequently, in order to exploit such opponents, your own baseline defense frequencies will need to be modified.
While this process can get technically complex, the good news is that, as is so often the case in poker, using your greater knowledge to stay a step ahead of your opponents will bring positive long-term results.
As emphasized in the first section of this article, the motivation behind the MDF is to avoid being exploited. Unfortunately, we have learned that this approach is incorrect in detail, and the construction of correct defense ranges is more complicated in practice. Understanding the theory behind this allows us to become the exploiter rather than the exploited.
What about playing against a perfect GTO opponent who has the sophistication to move beyond a MDF defensive strategy? Is it not the case that such an opponent is impossible to exploit? How will we ever squeeze a Sklansky dime out of such a poker deity?
The first point to note is that, despite what some players claim, there is no player that plays a perfect GTO strategy. This is in fact impossible, simply because no complete GTO strategy currently exists. Of more practical interest, however, is that those players attempting to emulate a GTO strategy leave themselves open to some simple exploits, as coach w34z3l explains in the following video.
We do not wish to minimize the challenges presented by opponents who have devoted hundreds of hours to studying GTO solver output. For one thing, it is likely they have analyzed many other areas of the game, and shown a dedication to their craft that inevitably leads to advanced poker skills.
The point is simply that no player is unexploitable, however they construct their defense frequencies or any other aspect of their strategy. By studying the frequencies of your opponents carefully, either through online stats or live approximations, you defend yourself against anyone at the poker table. It follows that you can find a profitable edge against any opponent.
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