Examining Formations Part 1: In-Position Offense

This post was originally published on Februrary, 28 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 finished running every script to populate the flop database I plan to use as the basis of my work. My PC was on overdrive for most of January as PioSolver ran day and night. When everything was done, I solved 184 flops for 32 different formations, finding an equilibrium solution for 5,888 flops to an accuracy between 0.5% and 2% (depending on the tree complexity). Some ran very quickly, such as this one, modeling a BB vs EP 3-bet pot:

Others, such as this SB vs BB single raised pot scenario, took much longer to complete:

While these scripts ran, I simultaneously looked at the outputs from the first few completed files. Using this data subset, I explored success metrics and examined and documented the rest of the data set. Now that the full data set is compiled, I’d like to start the data discovery process to see if I can find any initial high-level insights.

First, I plan to examine the interplay between ranges across various formations. I chose 32 common situations where we find ourselves at the table to populate the data set. These include single-raised and 3-bet pots, in-position and out-of-position spots, and offensive (uncapped) and defensive (capped) situations. I used my ranges for a perspective I could study for each formation. For the opponent, I started with Upswing’s published ranges and adjusted somewhat to account for (my perception of) the $5/$10 player pool in my local casino. This at least provides good estimates of realistic ranges to best model how each scenario should play in an equilibrium environment.

Quick disclaimer - I fully realize that this won’t derive the “optimal strategy” and the maximum EV I can earn against a typical player pool. I don’t plan to study this to attempt to mimic equilibrium strategies. I do believe that there is great value in studying the equilibrium environment. It can help us approximate frequencies and strategic actions across hand classes from which I can develop the foundation of a strategy. It can also help identify potential exploits in the player pool and areas in which we might be susceptible to counters. By understanding the equilibrium solution, we can learn a baseline from which we can deviate based on additional in-game information.

Starting at the macro level, I can aggregate the solutions for all boards at the formation level to look at how well each position performs in specific spots. Through this, I’m particularly interested in EV distributions and betting frequencies.

Now, let’s jump in and start looking at the first formation grouping: In-Position Offense.

In-Position Offense

These should be our best and most profitable formations. We arrive at the flop with an uncapped range and positional advantage against a capped range. We’ll be able to press equity and over-realize our equity very frequently.

For single-raised pots, this situation is exclusively us opening and facing a defender from the blinds. For 3-bet pots, we are either 3-betting an earlier position open from a late position or 3-betting the SB open from the BB.

These are the nine formations I chose to examine. I plan to add 4-bet pots shortly to this data set, but these cover the majority of situations we can find ourselves in at the table:

• Single-Raised Pots

  • Early Position open (UTG, UTG+1, UTG+2), called by the Small Blind

  • Early Position open, called by the Big Blind

  • Middle Position (LJ, HJ) open, called by the Small Blind

  • Middle Position open, called by the Big Blind

  • Late Position (CO, BTN) open, called by the Small Blind

  • Late Position open, called by the Big Blind

• 3-Bet Pots

  • In Position vs an Early Position open (UTG, UTG+1, UTG+2)

  • In Position vs a Mid or Late Position open (LJ, HJ, CO)

  • Big Blind vs Small Blind open

For each formation, I have aggregated the equilibrium values for Equity, EV, our share of the pot (EV %), EQR, and the strategic options for these formations if the villain checks or if he leads across all flops. I included large (66% pot) and small (33% pot) bet size options for offensive formations since we’ll have a range advantage on most boards, c-bet frequently, and multiple strategic options.

Single-Raised Pots

When looking at the data, one row immediately jumps out at me — the LP vs SB formation. From looking at the metrics and frequencies, it’s a clear outlier compared to the rest of the formations.

Below are the ranges and solution configurations within PioSolver.

Things aren’t bad for us in this spot. We are still in a position with an uncapped range; we over-realize our equity, and we earn more than 50% of the pot. However, this is the only formation in this group for which we have less than 50% equity. Our EV, EV%, and EQR are noticeably lower than the others within this configuration. This is represented in the equilibrium frequencies. The LP is much more cautious, checking back frequently, while the SB will have a 13% leading range across all flops.

I find this to be interesting and worthy of further investigation. Our LP range, while wide, is uncapped and contains the AA, KK, and AK. The SB does not have these hands in range. Much of its broadway region is also discounted by 50%, including QQ-JJ. So, while the SB does have a more narrow, condensed range compared to the LP width, I wouldn’t expect that to overcome the top-end disadvantage the SB range will face. As I dive deeper into our analysis, I plan to mark this formation as one to investigate, as there may be good opportunities to find exploits.

When removing the LP vs SB formation from the view, the other boards more consistently demonstrate our range and positional advantage combination. We have at least 50% equity on all formations. We also significantly over-realize this equity from all formations, with EQR values between 115% and 119%. As a result, our opponent will almost always check to us on the flop, only leading to us more than 5% of the time. Consequentially, we’re also betting more than 50% of the time in all formations.

As expected, there is a clear relationship between Equity/EV and our position. Logically, our range will be tighter and stronger as our position shifts to an earlier position. Since we’re opening a linear range, we’re only shedding hands at the bottom. This will result in higher equity and EV when facing the blinds, as our relative position is earlier. We can also bet slightly more as we trend toward this tighter EP opening range.

Our opponent’s position seems to have a more significant impact on our EV and strategic actions. For all 3 of our opening positions (EP, MP, and LP), we fare worse when facing the SB than the BB. That’s intuitive when understanding SB vs BB preflop calling ranges. The SB will naturally have a narrower range than the BB will. The SB cannot close action through a call and must account for the BB, who is yet to act when making preflop decisions.

For all formations, equity, EV, and EQR are lower when facing the SB than the BB. Unsurprisingly, the equilibrium solution is also aggressive less frequently. This is a good general concept to remember in single-raised pot scenarios. It’s sometimes easy to group the blinds and construct our ranges similarly against them collectively. However, there is a distinction between our EV and frequencies when comparing facing the two different positions. Even though we can still use our position to press equity, we should add more hands into our check-back range against the SB, as we can expect fewer air hands on the flop.

3-Bet Pots

Our advantages are amplified in 3-bet pot scenarios. Since ranges are narrowed, we have a lot fewer marginal hands. As a result, the equity edge of an uncapped range will almost always be much better than that of the capped opponent. When combined with our position and ability to over-realize equity, our opponents will almost always check to us (~97% of the time).

The most advantageous formation of the 3-bet situations is as an in-position 3-better against an EP open. Below are the ranges and solution configurations for this formation.

It might initially seem counter-intuitive to be most at an advantage when we’re against an EP open/call range compared to a formation where our opponent is wider. However, this makes sense when considering that our default 3-bet range in this formation is polarized, consisting of only our top-end hands and bluffs. In the other two 3-bet formations (IP vs a MP/LP open and BB vs SB open), we have a much wider, linear range. As a result, we don’t quite have as clear of a path toward polarization.

In the IP vs EP 3-bet pot situation, we have over 57% equity across all flops at equilibrium as the IP raiser. We will also over-realize our equity by 18%. This results in us capturing 68% of the pot across all flops. We should primarily bet most flops, often for a larger sizing. As I investigate further, I’ll want to understand possible outliers to this approach. These would be the boards on which I will struggle to press equity. If I can best identify those boards, I can only adapt to them and simplify my strategy execution across the rest of the boards.

The metrics for the other two 3-bet pot formations — IP vs a MP/LP open and BB vs a SB open — look almost identical. We have the same equity, capture a similar share of the pot, and have similar strategic actions. In these formations, we should generally bet. About 75% of our range bets in aggregate for these formations, slightly preferring the smaller sizing when it chooses to do so.

It also makes sense that these two formations might play similarly. Both opening ranges will be wide, and both 3-bet ranges will be linear. This may result in some similar dynamics. Because our frequencies and metrics are similar, we may find opportunities to save efforts and group these formations in our execution strategies.

Conclusion

In many ways, I think this process detailed above is an incredible representation of why I love learning more about this game. Within this analysis, I started exploring aggregate data across 184 flops. That’s at such a high level — I haven’t yet started dissecting the nuance of all the different types of boards we can face. But even at this high level, data analysis can uncover strategy guidance.

I started to explore some initial data points and came up with some concepts and ideas that I could utilize at the table. I also identified areas I should explore further to identify possible opportunities for exploitation. Overall, it was a productive exercise, and good progress.

Over the next few weeks, I plan to work through the other formations. In my next post, I’ll tackle formations in which we’re out-of-position on offense.

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

Thanks for reading.

-Lukich