Examining Formations Part 4: Out-of-Position Defense

This post was originally published on April 9, 2020, on my personal website, Lukich.io. I have since consolidated all of my poker-related content by reposting it onto Solver School.

This post is a compilation of a 4-part series published between February and April 2020.

Introduction

Quarantine life has been fairly challenging for me concerning my poker work. When stay-at-home orders began a few weeks ago, I thought I could spend more time on this site and my work. I planned to pump out 2-3 posts per week instead of my current pace of 1. After just a few days of home life, I quickly realized how wrong I was.

With both of my girls home and my wife also working a day job, I don’t often have any free hours during the day. My wife and I are both struggling to juggle work with taking care of the kids, trading shifts back and forth all day. This limits any time I can devote to other activities to evenings after my kids’ bedtime or the few hours I may get to myself on a weekend. I have a lot of priorities in my life — growing this site, obviously, but also playing poker (now online), spending time with my wife, exercising, or just relaxing and watching TV — that are competing for this time.

I am happy that I can still prioritize my work and this site, and I have still been making progress on my research. After these first few analyses, I’m excited about some initial findings. The data has been informative and has given me a sense of optimism about the strategic insights I may be able to develop or confirm.

From the beginning of this site, my goal has been to develop a data-driven strategy from preflop to river. I’m currently working on developing the flop component. To analyze my strategic options and develop a framework, I built a foundational data set. I have started the process of analyzing this data set and have been focusing on this over the past 6-8 weeks.

I started at a macro level, first examining data at the formation level. By doing so, I hope to identify those formations that play similarly. These insights may help to simplify some of my strategic development and uncover high-level concepts that can form a foundational element.

I split my formation work into 4 parts. I started with In-Position Offense formations, where we are the preflop aggressor and arrive at the flop in-position. Afterward, I wrote about Out-of-Position Offense formations, where we are the preflop aggressor but now arrive at the flop out-of-position. 2 weeks ago, I shifted over to the defensive side of the game tree and looked at In-Position Defense formations, in which we arrive at the flop through a preflop call.

These different formation types can be represented within the 2x2 framework below that I introduced at the beginning of this work:

Today, I plan to complete this analysis by exploring the one box we have not yet explored — defensive formations in which we are out-of-position — the bottom-right square.

Out-of-Position Defense

I saved this formation group for last for a reason. It’s the worst spot where we can find ourselves in no-limit hold’em — out-of-position without the initiative in the pot. Even the best players in the world will lose their fair share of pots in these formations. Overcoming position and range disadvantage requires a significant skill advantage.

The obvious question is — why would we ever choose to put ourselves in these situations? The answer is that we already have some money in the pot and usually get the right price to call preflop. These situations occur in single-raised pots when we call from the blinds or in 3-bet pots after our open is 3-bet by an in-position player.

Our ranges in these defensive formations are very capped — out-of-position, even more so, as we are less likely to retain premium hands as traps in a calling range out-of-position than if we were in position. The degree of this cap will depend on other players' specific positions and actions. However, our range won’t have some of the strongest preflop hands (AA, KK, QQ, AK, etc.). Our opponent will have full coverage of these combos in their uncapped range. As a result, we will be at a range disadvantage on most possible flops and will likely face a continuation bet.

We don’t have the advantage of position. Instead, we have to act first on the flop. Since we’ll be at a range (and equity) disadvantage on most boards, any aggressive actions will leave a large chunk of our range unprotected. While this is not necessarily bad, we will need an opportunity to polarize against our opponent’s range with the aggressive portion of our range. This is difficult to do so effectively when we’ll also often be at a nut disadvantage to our opponent.

Because of these reasons, our equilibrium strategies will be very passive. We often won’t have a leading range, checking a large portion of our range. When we check and face a bet (which will be frequently), we typically won’t raise at a high frequency, often preferring to call or fold. In other words, it’ll be challenging to develop aggressive strategies.

While these can seem like grim situations, it’s important to study them. These spots are inevitable when playing poker. It feels like we always play in these formations on some frustrating nights. In this case, money saved is just as good as money won. It all contributes to our overall win rate. Sometimes, this means making good folds, identifying good bluff catcher spots based on blockers, or knowing the best spots to counter-attack and the ones we should stay passive.

I chose seven formations below to examine within this set:

• Single-Raised Pots

  • We flat an early position open (UTG, UTG+1, UTG+2) from the small blind

  • We flat an early position open from the big blind

  • We flat a middle or late position open (LJ through CO) from the big blind

  • We flat a button open from the big blind

• 3-Bet Pots

  • We open from early position (UTG, UTG+1, UTG+2) and flat vs an in-position 3-bet

  • We open from middle position (LJ, HJ, CO) and flat vs an in-position 3-bet

  • We open from the small blind and flat vs a big blind 3-bet

The one thing that’s noticeably not in here is a small blind flat range against a middle or late-position open. When I started my research, I began developing preflop ranges at the end of 2019. At the time, I had subscribed to the thought that a better simplification is to 3-bet or fold from the small blind against one of these later position openers. I have since seen some S4Y data demonstrating the value of maintaining a flat range in these formations. I plan to redevelop my small blind ranges to include a calling range, but I haven’t yet had the chance to do so. When I get to that, I’ll update this part of my work.

Single-Raised Pots

Below are the metrics and strategic frequencies for single-raised pot formations:

When I first look at this data, the first thing that sticks out is that it all looks pretty poor. While we have an equity advantage in 2 of the 4 formations, we greatly under-realize our equity across all formations. As a result, our EV% ranges from 36%-42% of the pot.

Our strategic actions here do vary across the formations. When we are in the BB, our leading frequency increases as the opener’s position moves later. We virtually never have a leading range in BB vs EP formations at equilibrium, only leading 2% of the time. Against a BTN open, however, our BB range now leads 8% of the time at equilibrium. This makes sense when we consider that our opponent’s density of hands with poor equity that completely miss the board will increase as their range becomes wider, allowing us to target a portion of his range effectively.

The leading frequency is even higher in the SB vs EP single-raised pot formation. The solver leads 11% of the time at equilibrium within these formations. This is presumably because our SB flat range is very narrow, so we will have some boards that it connects with significantly, letting us play our range aggressively. Based on the trends above and the other SB data I referenced, I would guess that the SB leading frequency will also increase as the original raiser’s range shifts to a later position.

The next interesting thing is that check/raise frequency is inversely correlated with leading frequency within the data set. In the BB vs EP formation, where we only lead 2% of the time, the solver chooses to check/raise at 12% frequency when facing a bet. Conversely, the SB vs EP formation has an 11% frequency of leading and only a 5% check/raise frequency.

I think that this is more interesting when you sum these values together. If you add up all our strategic actions, you’ll notice that the Check/Raise, Check/Call, and Check/Fold frequencies don’t add up to 100%. They add up to the total Check % from our first decision of Bet or Check. When adding the betting frequency to this total, we get the full picture of what the solver does at a 100% frequency.

When I combine the leading frequency and the check/raise frequency, we can see the total frequencies below. I’ve demonstrated this as our total aggression frequency (leading frequency plus check/raise frequency):

From here, we can see that our range is taking an aggressive action between 13-17% of the time at equilibrium. There are some correlations between position and our total aggressive frequency — when we face a later position open, we can bet more frequently. However, it’s not significantly different from one another. It suggests that we should approximately be aggressive at similar frequencies when out of position, but should shift these frequencies towards either side — check/raises or leads — more often based on some formations.

The other 83-87% of the time that we play our hand passively, we split between check/calls and check/folds. When playing as the BB, the solver chooses about a 1:1 ratio of calls to folds against early position. Against a wider MP or BTN range, the solver chooses closer to a 4:3 ratio of calls to folds. When playing as the SB against EP, the solver calls at about a 5:3 ratio. While the EP range is strong, the SB will have less width to its range, increasing the likelihood that a particular combo has decent equity.

Our opponent should be betting between 60-70% of the time at equilibrium in these situations when we check. It’s important to consider player pool tendencies to understand how to develop exploits against people who deviate significantly from these frequencies. I should be able to develop more leading ranges to counter those that bet too infrequently and more check/raise ranges to counter over-bettors.

3-Bet Pots

Things weren’t that good at equilibrium in single-raised pot scenarios. They’re downright terrible in 3-bet pots. Below are the metrics and strategic frequencies for these formations:

Our equity is poor, ranging from 39% to 43%. We are not incentivized to play a high SPR pot out-of-position with the better portion of our range. So, we should develop more polarized 4-bet ranges when out-of-position. As a result, our calling range in these spots will be less protected and more capped than it might be if we were in-position.

In addition, both ranges are much narrower in 3-bet pots than in single-raised pots. Consequently, our opponent’s nut advantage on many boards is also a higher density of their range. I demonstrated this last week, but we can visualize this using the EP vs IP formation as an example in the graphic below:

Many of our opponent’s range consists of premium hands that are not within our range. His 3-bet range against our EP open is narrow, only containing 63 combos. Unfortunately, 45% of that range consists of AA, KK, and AK — 28 premium combos that we don’t retain in ours.

Because of these factors, our opponent can bet much more frequently. In these formations, he can bet at over an 80% frequency. This means we’re unlikely to find exploits against an opponent that bets too much. We should develop a baseline strategy as if our opponent will bet and adjust against players that check back at a higher frequency.

Since our opponent is betting more frequently and pressing their significant equity advantage on ours, we must fold at a higher frequency. The solver check/folds at 55% frequency with our EP range at equilibrium. In the MP vs IP and SB vs BB formations, the check/fold frequency is slightly lower at 47%-48%. Ranges are wider in these formations, and the density of the preflop 3-bettor’s nut advantage is not as high as in the tighter ranges in the EP vs IP formation.

Since our opponent is betting at a high frequency and we’re often folding at equilibrium, we will under-realize our equity because we are forced to shed some hands that may have wanted to continue had we played utilizing a strategy based around minimum defense frequency. Our EQR is poor in these spots, ranging from 69%-77% — this metric correlates with how frequently our opponent bets.

Poor equity and EQR values mean that we’ll earn a small percentage of the pot at equilibrium — between 27% of the pot in the EP vs IP and 33% of the pot in the MP vs IP formations. With these low baseline results, we can see our uphill battle. We will unlikely become net winners in these formations even if we exploit our opponents. As such, our job is to try to realize our equity as best as possible and attempt to capture closer to 50% of the EV in these situations.

The solver rarely leads at equilibrium in 3-bet pots, choosing a 5% frequency in EP or MP and a 2% frequency in the SB. Some check/raising in these formations mirrors the same phenomena we saw above. The solver chooses our low 2% SB leading frequency paired with a higher 10% check/raise frequency. The other two formations check/raise at a lower 6-8% frequency.

Overall, we should be less aggressive in these formations in 3-bet pots than we are in single-raised pots. Our aggression frequency ranges between 10-13% in these formations as demonstrated by the table below:

The other 87-90% of the time, we should be splitting to fold more frequently at equilibrium. With our narrow EP range, the solver chooses a 3:5 ratio of calls to folds. In the other two formations, the solver chooses a 4:5 ratio.

While the initial data looks grim in these spots, I’m pleased by what I see. In the single-raised pots and especially in our in-position formations, our opponent bets less frequently at equilibrium. We could then identify potential player profiles that bet too much or too little compared to these equilibrium frequencies. This requires an understanding of at least three different strategies for playing a situation — our baseline strategy, our exploitative strategy vs someone who bets too frequently, and our exploitative strategy vs someone who bets too little.

In these 3-bet pot formations, it’s difficult for our opponent to bet too frequently. Even if they do, it’s unlikely that simplifying their strategy to bet 100% of hands would cost them that much EV. As a result, we can eliminate one exploitative counter and only develop an exploitative strategy vs an under c-bettor alongside our baseline strategy.

Conclusion

Some of the conclusions I can make today are similar to those in my last article on defensive, in-position formations. Specifically, we are more likely to under-realize our equity in single-raised and 3-bet pots when playing in the defensive game tree. Additionally, as SPR gets smaller in 3-bet pots, our opponent will have an increased nut advantage density. This will decrease the impact of position and allow our opponents to bet much more freely, forcing us to play a defensive, realization-focused strategy.

Many of these challenges are amplified when we don’t have the advantage of position. When forced to act first, we allow our opponents to check back and realize more of their equity by seeing a turn card or to capitalize on their range advantage through a bet. This will increase our challenge of realizing equity and cause us to fold more frequently.

This wraps up my 4-part study on formations. From here, I plan to examine how flop characteristics can impact our equity, EV, and strategic frequencies. I have done some work on this in the past. At the beginning of 2019, I conducted a regression analysis to quantify this. I’ll leverage some of that, but I think I can build on this work over the next few months.

If you have any comments or thoughts, please feel free to leave any comments below. You can also contact me at [email protected] or on Twitter or YouTube through the links in the footer below.

Thanks for reading.

-Lukich