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How Important is Balance?

It’s all the rage in the modern poker world. Finding balanced solutions to poker hands using GTO solvers. It’s a powerful feeling knowing that there is nothing our opponent will ever be able to do in order generate an effective counterstrategy against us.

Is it really as powerful as it sounds? However, in this post, we’ll discuss the implications of balanced strategy and why arbitrary balance can be more damaging than useful.

 

What is Balance?

The average player does not understand the concept of balance accurately. Sure, many players understand that balanced play cannot be exploited, which is completely true. A balanced play does indeed guarantee a minimum winrate. However, problems tend to creep in after exposure to the following statement.

Balanced play does not necessarily imply lower EV lines.

For example, many players might believe that we choose to play certain hands in our range at a lower expectation in order to benefit other holdings in our range. This is absolutely not what balanced play implies. After all, it violates one of the fundamental principles that the best players abide by – Always play every hand at its highest EV.

After all, how does deliberately lowering the expectation of a holding make our strategy better? Surely it makes our strategy worse! Any benefit that other holdings gain will in no way compensate for our loss of EV by deliberately taking a lower-EV line with certain holdings in our range.

This typically confuses players further because they have the belief that all players must consciously choose between balance and exploitation. (As if it’s a stylistic choice that is presented to us). In truth there is never really any choice in the matter, there is always only one decent option that presents itself. Take the line with the highest expectation. If we ever find ourselves playing a balanced strategy, this is because that strategy is a by-product of always taking the line with the highest expectation against a certain opponent.

A Product of Maximal Exploitation

The idea that a balanced strategy could be the by-product of taking maximally exploitative lines can be difficult for many players to grasp. This is because they have the pre-conceived idea that balance and exploitation are polar opposites.

Imagine for a minute our opponent is playing a perfect GTO strategy. What is the counter-strategy that produces the maximum expectation? Another misconception here is that “it doesn’t matter what we do, our EV will be the same”. While this may be true in certain specific scenarios, it is absolutely not true across our whole strategy. Just because our opponent is playing a perfect GTO strategy does not imply that we can’t make our winrate worse through utilization of a bad strategy. (Don’t believe me? Imagine we never bet ourselves, call all bets from our opponent, then proceed to open-fold every river regardless of whether we face a bet or not).

The implication here is that there must be a strategy which generates the maximum expectation against a perfect GTO opponent. Perhaps you already sense the answer here; it is to play a perfect GTO strategy in response. We should hence immediately see the link here between GTO play and maximally exploitative play. A GTO solution to the game of poker just so happens to be the maximally exploitative strategy against another perfect GTO opponent. We absolutely don’t look to randomly employ this strategy for the sake of “balance”; we would employ it only when it’s highest EV to do so! This has always been our goal, to generate the highest expectation.

Play vs Non Perfect Opponents

Now let’s imagine our opponent was mostly playing a solid GTO strategy, but he had this issue where he calls too many rivers. We can continue to play our balanced GTO strategy or we can attempt to increase our expectation by cutting out some of our river bluffs.

This would naturally mean we are weighted towards value-hands when we fire the river, but is this really a problem? It’s true that we are open to counter-exploitation, our opponent could adjust by folding rivers more frequently. However, it’s important to keep the following in mind.

– We have no way of knowing whether villain will ever adjust.
– By bluffing the river against a non-folder we are not taking the max-EV line.

By sticking to a GTO strategy we are essentially violating one of the fundamental rules of poker (always take max-EV lines) purely based on a hunch that our opponent might show the propensity to adjust. Keep in mind that relevant adjustments are rare. More than likely villain will continue to call too wide on the river.

Even if villain does adjust (folding more rivers), so long as we can counter-adjust (bluffing more rivers) the generated expectation will still be higher than following an equilibrium (balanced) strategy.

The following is a rough representation of a preflop discussion I often might have with a student. This usually occurs after the student makes a speculative preflop bluff against a non-folder. For example, imagine BTN opens and hero 3bets 75s in the BB. Villain doesn’t fold much preflop or postflop.

Coach: What’s with the 3bet?

Student: It’s a bluff, it’s in the preflop ranges.

Coach: Ok, but villain doesn’t fold to 3bets…..

Student: Right….but if I only value-3bet him then he’s going to figure that out and start folding a lot. I need to make sure I have some bluffs in my range, it makes my value-hands higher EV. Basically, he’ll have to call down wider because he knows I can show up with the 75s some of the time.

Coach: …………(facepalms quietly)

So how should the coach answer? What is the problem with the student’s reasoning here? The problem here is that the student is propagating the idea that it is ok to play hands with a negative expectation in order to benefit other hands in our range. Let’s list the problems with that –

– There is no reason to believe that villain will “figure out” anything. Most of the time he’ll continue to play the same strategy.

– We are losing money in the short-term by taking -EV lines. There is no guarantee we’ll ever get this money back. Even if we win some back, it won’t be enough to compensate for the -EV lines we took previously.

– It’s not a big deal if villain starts folding more, we’ll simply start including the relevant bluffs in our 3betting range. But we’ll make this adjustment only after it is max-EV to do so.

So initially, we will 3bet a value-heavy range with zero bluffs. If villain never adjusts, this is fine, we are generating the max EV against his static strategy. If he adjusts we will counter-adjust. Notice that at every point we will be generating the highest expectation. If villain learns to play better poker and plays perfectly preflop, we will also adjust to our best approximation of a perfect (balanced) strategy. Notice how we only balance when it is incentivized by our opponent. If balance is not incentivized, it means that we are not maximizing our expectation by balancing.

Incentive to Balance

Let’s take a slightly more advanced example to illustrate the concept of incentive to balance. Imagine that we are playing OOP on the flop as the PFR. This is a common spot where the average player check/folds way too frequently after checking. Let’s imagine we have a reasonable holding and we are deciding whether to c-bet or check/defend. Most players have a strong tendency to cbet all of their good hands in these type of situations, which is exactly why they struggle to defend their checking range.

So should we put some strong hands in our checking range to balance? Perhaps, but only if that balance is incentivized. Never balance for the sake of it! Take a moment and think – what type of strategy could our opponent employ that would incentivize us to defend our checking range with strong holdings? Well, he could start playing hyper aggressively against our checks. After all, this would make sense as an exploit for him if he felt we where folding too frequently after checking.

In fact, if villain played sufficiently aggressively, we wouldn’t be incentivized to bet anything. Most, if not all hands, could be played with a higher expectation as either a check/raise or a check/call. Even so, this wouldn’t be a balanced strategy either, it would still be a heavily exploitative one. Good players may then enter into a period of iteration where they come closer and closer to playing a balanced strategy. Villain stops stabbing so aggressively because he is experiencing relentless check-raises. We start c-betting a bit more aggressively because villain is getting to realize a lot of free equity with his flop checks. This leaves our checking defending range weak again (but not as weak as before). Villain stabs aggressively again (but not as aggressively as before). We start shifting more hands into our checking range again but leave a larger amount as c-bets than before.

Note that all of this jockeying has nothing to do with balance – it is all to do with exploitation. But as two good players iteratively attempt to counter-exploit each other the by-product is that they get closer and closer to equilibrium strategies. In fact, it is even possible to search for GTO approximations using this method in tree-building software such as CREV. We can repeatedly solve for the max-exploit for player A, then player B, player A again, player B, and so forth. In many scenarios, the more iterations that are run, the closer we are to an equilibrium solution. Of course, this is unnecessary in practice since CREV also has an equilibrium solver, but it helps us to understand more about the relationship between exploitative and equilibrium play.


How Important is Balance

As an extrapolation on the discussed principles, it would be reasonable to conclude that balance is not at all important. It’s merely a by product of good players going head to head, but it is not something to be sought after directly.

As we have seen, this is not how the average player approaches balance. They instead attempt to arbitrarily bring balance to their game without asking why, and without questioning whether they have an incentive. They are perfectly content to take -EV lines if it makes them feel more secure about the overall structure of their strategy. We could refer to this as “balancing for the sake of it”.

So we should understand that this post is not a discussion on exploitation vs balance. Those type of discussions are popular, but in truth, they shouldn’t even exist. No good player has ever cared about balance unless it was incentivized through a promise of generating a higher expectation. The elite lives by the golden rule – Always play every hand at it’s max EV.

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