Examining Formations Part 3: In-Position Defense

This post was originally published on March 26, 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

I have studied my flop data set over the past few weeks. Before diving into more specificity, I wanted to start at the highest level, so I am examining the formation level. I have devoted two posts to exploring offensive formations.

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, in which we are the preflop aggressor but now arrive at the flop out-of-position.

These two posts are represented by the two boxes on the left side of the 2x2 grid below:

Now that I have completed looking at the offensive game tree, it’s time to move to the grid's defensive (right) side. The difference between these formations and the offensive ones is that we now arrive at the flop as the preflop caller. In today’s post, I plan to look at the defensive formations in which we retain position — the top-right square.

In-Position Defense

As I’ve demonstrated, we can bet more frequently when we have an uncapped range, and our opponent has a capped one. This situation often happens when we arrive at the flop through the aggressive game tree. Through that lens, we often looked at ways to capitalize on equity through betting. However, we have yet to explore a whole other side of the game tree — the defensive lens, in which we now need the ability to realize equity and counter effectively.

We arrive at the flop as the preflop caller in defensive formations. In the majority of circumstances, this will cap our range. While the degree of the cap will depend on the specific positions and actions of other players preflop, it means that we won’t have a portion of the strongest preflop hands in our range (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.

Fortunately, in this set of formations, we at least have position on our side. So, while we will frequently be at a disadvantage from an equity standpoint, we will often over-realize our equity. Our opponents must respect this positional disadvantage and check more often than they would otherwise.

In practice, however, many live players don’t understand this nuance and aggressively bet expecting overfolds. In many live cash games (even tough ones), the out-of-position aggressor doesn’t slow down and checks more frequently. I will dig into the data below, but betting frequencies tend to be higher in practice than they should be at equilibrium. This imbalance can create excellent opportunities for us to exploit. Some formations below offer us the greatest opportunities to find specific exploits to exploit our opponent’s mistakes in-game.

I chose seven formations below to examine within this set:

• Single-Raised Pots

  • We flat an early position open (UTG, UTG+1, UTG+2) in-position (usually also early position) with an uncapped range

  • We flat an early position open in-position with a capped range

  • We flat a middle or late position open (LJ through CO) in-position with a capped range

  • We flat a small blind open from the big blind with a capped range

• 3-Bet Pots

  • We open from early position (UTG, UTG+1, UTG+2) and flat vs a small blind or big blind 3-bet

  • We open from middle position (LJ, HJ) and flat vs a small blind or big blind 3-bet

  • We open from late position (CO, BTN) and flat vs a small blind or big blind 3-bet

As with all the other formations I have previously explored, I have aggregated the equilibrium solutions across all 184 flops within the subset for Equity, EV, our share of the pot (EV %), EQR, and the strategic options for these formations if villain checks or if he leads across all flops. For these defensive formations, I only chose one bet size option (50% pot), since we’ll be at a range disadvantage and likely won’t have as many aggressive strategic options.

Single-Raised Pots

I want to split the analysis of these formations into two groups. The first is the first two rows, a preflop raise from early position. The second is the bottom two rows, a preflop raise from a later position (or small blind) with a wider range.

Responses vs Early Position Opens

When looking at the entire set of formations, one row immediately sticks out — the EP vs EP formation. It might appear to be an anomaly, but the data is accurate. However, this should be much more obvious when we look at the solver configuration below:

In my Poker Out Loud Episode 4 recap, I introduced the idea of retaining an uncapped flatting range against an early position open. As discussed in that article, I sometimes choose to deviate from a baseline raising strategy and take a flat-only strategy against an open EP. This is certainly not a default play, but I think this deviation can be very profitable when playing in active games with other capable players who understand range construction and will be actively trying to learn and exploit my strategy.

There can be some great benefits from playing this way. I covered a few of them in that article, but a common theme is deception. We can see part of the impact this strategy can have by comparing the metrics for the EP vs EP formation to the IP vs EP formation:

As we can see from the data, we retain more equity, earn a higher EV, and realize equity more efficiently when we retain an uncapped range. This isn’t particularly interesting when we understand both ranges' solver configuration and shape. What is interesting, however, is seeing the equilibrium response from our opponent in these two rows and comparing it to what we would expect to see in-game.

When we compare the solver configuration above to the second formation below, in which we have a polar 3-betting strategy, we can see that our opponent has the same opening range for both. The only difference between the two inputs is our calling range. What’s more significant is that unless our opponent knows us very well, our opponent won’t know that we have an uncapped range and will often assume we are more capped. This would suggest that they will likely play us as if we have the range represented by the 2nd formation, not the first.

At equilibrium, our opponent should continuation bet 33% of the time and check the other 67% of the time in this IP vs EP formation with our capped preflop calling range. When our opponent does lead, our equilibrium response is to raise with a polarized 11% of our range, call with 54% of our range, and fold with the bottom 35%. For the two-thirds of the time our opponent checks to us on the flop, we should check back about half the time at equilibrium.

I would argue that many villains will continue to bet at a higher frequency in practice than they theoretically should at equilibrium in this IP vs EP formation. From my experience, opponents will bet at greater than a 33% frequency. As a result, I should be able to identify and develop counter-strategies in specific spots through further data exploration. I think we should have opportunities to raise a wider, linear component of our range on various flops.

This exploit will be amplified if we retain an uncapped range, as demonstrated in the EP vs EP formation. At equilibrium, our opponent only continuation bets at a 9% frequency within this formation. When they do bet, our strong range continues at 70% frequency, mostly through calls. If our opponent is likely betting too much when they think they are facing a capped range, they are almost certainly betting significantly too much when we have an uncapped range. We can then develop more exploitative responses in our construction to take advantage of the betting errors we are facing.

Responses vs Middle/Late Position Opens (Wider Ranges)

I choose to group the other two formations because the data looks similar.

We earn almost the same amount of the pot in both formations, with EV % values of 44-45%. Our equity is lower in the BB vs SB formation, but we realize equity more effectively in the IP vs MP/LP formation. The equilibrium frequencies in our opponent’s and our strategic actions are similar when comparing the two formations.

The data in both formations look similar because the shape of both defense ranges is comparable. If you recall from examining in-position, we explored the 3-bet ranges against wider ranges. We can expand our 3-bet range linearly to attack our opponent in these situations. In doing so, however, we shift some of the top-end linear hands out of our flatting range, increasing our likelihood of capping our range. We take a linear 3-betting strategy in both formations, so it’s not surprising that the strategic actions taken at equilibrium are similar.

Our opponent should continuation bet at about a 50% frequency in these situations at equilibrium. Our response to the equilibrium should be to continue with about 2/3 of our hands, raising ~10% of the time with a polarized range. When our opponent checks, we should be betting a little less than half of our range as a response.

While the data looks somewhat different between the two groups of formations, I think there is one similar takeaway. From my experience, many players (both strong and weak) continuation bet too much out of position. Even against our more capped ranges above, our opponent should be checking half the time at equilibrium. In practice, I think opponents continuation bet more frequently than this. As I dive further into the flop data, I will plan to further explore exploitative responses to higher continuation betting frequencies in these formations. I believe we can develop counter strategies to take advantage of our positional advantage and gain additional EV from our opponents.

3-Bet Pots

Our strategic options from 3-bet pots appear to be somewhat simpler than in single-raised pot formations from looking at the data, although not in a good way. In all of the formations I have chosen to explore below, we open and are 3-bet by one of the blinds:

As you can see from the table, we earn a smaller percentage of the pot than in the single-raised pot formations. In all three situations, our range has less than 40% equity. In addition, we also under-realize our equity to a greater degree. As a result, we earn less than 38% of the pot — only 33% in the EP formation. We can see the effect when examining our strategic action frequencies. Our opponent gets to do much betting at equilibrium without much we can do to combat it.

Despite having position, we are simply at a greater disadvantage in these 3-bet pot formations as the caller. There are two primary reasons why.

The first reason is that both players’ ranges are narrower and contain fewer total hands. In these instances, each combo contributes more weight to the overall range. Specifically, the top-end hands that we don’t have in our range that our opponents have in theirs (AA, KK, AK, etc.) are a much greater portion of our opponent’s overall range.

I can visually demonstrate this phenomenon by comparing the LP vs BB 3-bet pot formation to the IP vs MP/LP single-raised pot formation above.

The left chart visualizes the IP vs MP/LP single-raised pot formation. Our opponent has 398 hands in their overall range. Their range is uncapped, while we retain a capped range. This includes the 130 stronger combos below that they have in their range that are not in ours. Of the 130 stronger combos, 18 are premium pairs earning the most EV.

The right chart visualizes the LP vs BB 3-bet pot formation. In this example, our opponent only has 104 hands in their overall range. Their uncapped range now only contains 38 stronger combos that we don’t. It also contains 18 premium pairs, earning significant EV.

The difference between these two situations is that in the 3-bet pot example, the stronger hands represent a greater percentage of our opponent’s overall range. 37% of the strongest combos in our opponent’s range are not present in ours, compared to 33% in the single-raised pot example.

To amplify this effect, premium pairs, such as AA, KK, and QQ contribute most to EV. These hands represent an even greater percentage of our opponent’s range in the 3-bet pot formation. 17% of their range in 3-bet pots are these premium pairs, while they only account for 5% of the range in the single-raised pot formation. In other words, our opponent’s nut advantage is amplified by the density of strong hands they have in their overall range. This causes us to be at a greater disadvantage within the hand.

The second reason we are at a disadvantage is because SPR is smaller. The SPR, or stack-to-pot ratio, measures the effective stacks in relation to the current pot size. It’s a concept widely popularized in the excellent book Professional No Limit Hold’em, by Matt Flynn, Sunny Mehta, and Ed Miller.

If it’s not immediately clear why a larger SPR would increase the value of position, consider the following examples:

• An SPR of 1 requires 1 pot size bet to get all-in

• An SPR of 4 requires 2 pot-sized bets to get all-in

• An SPR of 13 requires 3 pot-sized bets to get all-in

This can continue, but the point is that as SPR becomes larger, more bets (and more decisions) are required before all the money in the stacks is in the middle. This leaves more room for players to maneuver and outplay one another. While skill certainly greatly impacts any ability to capitalize in deeper SPR situations, the net benefit (with all things being equal) will go to the player in position.

In the single-raised pot examples I examined above, SPR is greater than 20. This means that even three full pot-sized bets won’t get all the money in the pot. In these 3-bet pot examples, SPR is about 6.5, letting us get all the money in with 2 slight overbets or 3 less-than-pot-sized bets. This simplifies decisions somewhat and reduces the impact positional advantage can have in gameplay.

When looking at the data, our metrics worsen as our absolute position is earlier — Our early position open/call range performs worse than our middle position open/call range, which performs worse than our late position open/call range. This is mostly because our opponent will 3-bet us more widely as our opening range widens. As a result, the density of their top-end hands decreases the wider they 3-bet.

At equilibrium, our opponent should bet very frequently. In all three formations, the equilibrium strategy for our opponent’s continuation bets over 80% of the time. When we face a lead, we can fold around 40-50% of our range and should rarely develop a raising range. We can likely eliminate developing raising ranges on most boards, simplifying to a call or fold strategy.

In the rare instance our opponent does check, we continuation bet more frequently from early position. When our opponent checks and weakens their overall range, we’re better able to attack them when we have our more narrow early position range.

While these situations are difficult to play, it doesn’t necessarily mean that we don’t have opportunities in these pots. We can capitalize and exploit our opponent's mistakes, sometimes for significant EV. It’s a reality that we’re inherently starting at a bigger disadvantage in these formations. It’s important to realize this and understand that we can also increase our win rate by losing less money over the long run in these spots.

Conclusion

If one thing is abundantly clear from these scenarios, position is very important. We tend to put much weight on arriving at the flop through the offensive or defensive game trees. When players have initiative, many think they should continue betting at a high frequency, regardless of their position. As I demonstrated above, that can be problematic when out-of-position, particularly when SPR values are higher.

The data also shows that two factors that arise in 3-bet pots, lower SPR values and increased nut advantage density in the preflop aggressor, can decrease the impact position plays. Our opponent can bet much more freely in these scenarios, and we are forced to play a defensive, realization-focused strategy.

In my next research post, I’ll finalize this series by exploring the worst formation of all — defensive, out-of-position situations.

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