Data-Driven Poker Strategies: How to Measure Success

This post was originally published on January 26, 2020, on my personal website, Lukich.io. I have since consolidated all of my poker-related content by reposting it onto Solver School.

Much of my current work is on the flop. I started to work on developing my flop strategies about a year ago. After putting it on hold to shift to other interests during the 2nd half of 2019, I picked it back up in 2020. I want to develop better ways to quantify the components of range advantage. More importantly, I want to be able to distill any findings into concepts that I can implement at the table. Because of the large scope of this work, I can’t simply look at a bunch of individual solutions. While examining the details can be valuable in some instances, it’s far too difficult to extrapolate findings from a specific flop into macro-level concepts that I can apply broadly. Instead, I need to take a top-down approach and look at many flops. In other words, I need a data set.

Luckily, I built a new PC specifically to run solves in December. Over the past 2 weeks, my computer has been constantly running Pio. I’m solving a 184-flop subset across 20-30 different formations (e.g. late position open flatted by the big blind, big blind 3-bet vs an early position open, etc.). While I’d ideally have a comprehensive database across all flops, solving every flop for every formation would not be efficient. There are 22,100 possible hold’em flops, 1,755 of which are strategically different. The 184-flop subset is a sample that represents the entire game, so I can utilize it as a proxy to model all flops. While I may return to increase this database later, the 184-flop subset will be the foundational data set I will use to model flop strategies.

As I build my data set, I can examine its structure to organize my work. When analyzing data, the worst thing to do at the start is to dig into it aimlessly to look for “ah-ha” moments. Trying to “find insights” in data without a plan or hypothesis is like finding a needle in a haystack. It’s critical to have a direction by developing a hypothesis and asking specific questions I can try to answer. I’ll expand more on this process in upcoming posts.

First, I want to talk about the other prerequisite before jumping into any data analysis — understanding the contents of our data set and developing a measurement plan. After all, to develop a hypothesis that can be answered using our data set, we first need to know its composition and how we can quantify success.

The image above is a 10-row sample from a table within the database that will ultimately make up the foundation of this flop work. It is an output from PioSolver’s aggregated data report output and represents an equilibrium solution for this formation with two approximated ranges. Each row contains key metrics from a specific flop solution for a formation — these ten rows examine 3-bet pots in which an early position player opens and calls a 3-bet from an in-position player. The action at this particular game node is on the OOP player (the early position raise/caller) on the flop.

Within this data set, I first want to explore the various metrics we can choose to measure success and the advantages and potential drawbacks of using each. From there, we’ll be able to determine the relationships between these metrics and how they interact with the characteristics of different boards.

I’ll eventually get into the details of all these columns. But for this particular post, let’s focus on column 4 (OOP EQ) through column 9 (IP EQR). Even though there are six rows, there are three unique metrics. The OOP and IP prefixes denote the players in the hand (out-of-position = OOP; in-position = IP). The three metrics we’ll look at to gauge success are:

• EQ - Equity

• EV - Expectation Value

• EQR - Equity Realization

Each of these metrics can be utilized to tell us different things about how our range interacts with our opponent. To determine how to use each as a success measure, it’s important first to understand how they are calculated and how to interpret them.

Equity

Equity is a simple metric. It represents a range’s likelihood to win at a showdown against 1 or more ranges (note: a range can be composed of 1 or more hands). Equity calculators are nothing new. Many will remember using PokerStove in the mid-2000s as their equity calculator of choice. It could be utilized to measure the equity of a hand vs a range, a range vs a range, a range vs a hand, or a hand vs a hand. Today, there are several good options on the market to calculate equity, such as Flopzilla, Equilab, and others.

Specifically, equity measures how frequently a range would win the pot if there were no actions for the rest of the hand. This will always be a number between 0 and 100; the OOP EQ + IP EQ will equal exactly 100.

Equity is particularly great to conduct range vs range analyses because it can quickly give us a sense of how we fare against an opponent’s overall range. It’s also really easy to interpret. Values above 50% mean that we’re a favorite and below 50% mean that we’re an underdog. We can examine this number to understand our overall advantage or disadvantage. This can help us start to develop betting strategies. Looking at the data above (a range vs range analysis), we can see values as low as 27% equity, showing us that our range for some of these situations fares very poorly against our opponent’s.

Equity can also be misunderstood at times. I believe that many read the first part of the definition — equity measures how frequently a range would win the pot… — and ignore the last — …if there were no action for the rest of the hand. It is important to understand that equity does not measure how often we will win the pot because it does not account for further action. To put it another way, if our range has 25% equity vs our opponent’s, that doesn’t necessarily mean that we will win the pot 25% of the time. It is up to our abilities at the table to win the pot at least this often.

Equity should be a guide in our strategy. Our goal should be to make the appropriate investments throughout a hand that will let us profitably realize (or over-realize) our equity. However, because equity doesn’t measure the impact of our actions, it can’t tell a complete story. We will need help of another metric to quantify this.

Expectation Value

While equity is our guide in strategy development, maximizing EV is our mission. EV represents the amount of money we can earn from every decision, so our priority should (almost) always be to maximize this value.

EV measures the expectation in chips (or dollars, blinds, or any other monetary value) for a specified range at the current point in the hand. For an individual hand, EV calculations can be done by hand. As we expand into range vs range evaluations, calculating manually is far too complicated. So instead, we use the help of a solver to determine EV. Unless we node lock individual decision nodes, EV values are based on an equilibrium output from the solver (with a small margin of error). Those equilibrium values will always depend on a set of parameters we define for the calculation. The data above is modeled as a $5/$10 game. The EV above represents the expectation in dollars for situations within this particular game — the value above can be divided by 10 to see the EV in big blinds. The EV number will always be less than the flop pot size ($295 from the 3-bet pot examples above). The OOP EV + IP EV will also equal exactly the flop pot size, as the players are splitting the current pot.

I don’t need to explain why EV is a great metric to measure. It’s fairly easy to understand that we want to maximize our earnings. However, like all metrics, there are better spots to utilize it as a success measure than others.

EV is outstanding when utilized to measure the effect of deviations in our strategies. For example, the EV values above are based on equilibrium outputs for a set of inputs. However, I could test how changes in my assumptions affect the EV as I develop my strategy. How does widening our opponent’s range change our strategy and the resulting EV? How does widening our own range change things? What happens if we adjust our sizing, our frequency, etc.? We can use EV to quantify the impact of any of these changes, helping us develop actionable strategic adjustments backed by data.

The drawback of relying on EV is that the potential error becomes more significant as our clarity in the inputs reduces. I think it’s worthwhile to explore the human-generated inputs that go into the calculation of EV:

• Both players’ ranges - We are probably confident in defining our own range and can estimate it fairly accurately. We will usually have much less clarity over a villain’s range. We can approximate some ranges based on player pool tendencies or specific profiling, but there will always be a margin of error. Other players do not think exactly like us and will construct their ranges with different (or no) logic.

• Strategic Actions - While we can at least somewhat estimate ranges, accurately determining strategic actions is impossible. Every decision made in the hand will impact the overall expectation. This includes how much to bet and how often to bet each sizing or check for every combo in a range at every decision point. When estimating these values, we can choose a few options to account for common situations. However, other strategic options may yield different EV values.

While range assumptions also impact equity, strategic actions don’t. Thus, our potential margin of error in EV calculations is more significant than equity calculations.

Despite the potential limitations, EV and Equity are excellent metrics that can inform our strategy differently. They are also combined to derive the third success metric.

Equity Realization

As mentioned above, we can determine our Equity EV by multiplying our equity share by the current size of the pot. This would be the dollar amount our range would be entitled to if we checked down to the river, fully realizing both range’s equity. This value can be indexed against the EV value generated by the solver. The ratio of our EV to our Equity EV measures how much we can over- (or under-) realize our equity throughout strategic decisions within the equilibrium solutions.

EQR is an interesting metric in that it’s dependent on both Equity and EV. Therefore, its accuracy depends on the same inputs and is subject to the same assumption challenges both Equity and EV do. However, EQR is a very useful metric for us to examine as it is a great proxy for our playability on a particular board. It can help to inform us of specific strategies for our play in a hand.

It’s important to note that EV impacts EQR and therefore, the strategic actions within the equilibrium solution. This means that we will naturally over-realize most of the time when in position and under-realize most when out of position. Therefore, in addition to looking at EQR as a standalone value, it should also be compared against the other boards within the same formation to determine its relative significance.

One More Metric to Monitor — Nut Advantage

The final metric I’d like to explore is one that’s not detailed above but does impact our ideal strategic options on the flop. That metric is the relative nut advantage one range has over another. The concept of nut advantage is clear. If our range holds more combos of the nuts than our opponent’s, we will hold the nut advantage and can usually apply more pressure through bets. However, to utilize this concept in our analysis, we must define it quantitatively. Pio doesn’t define nut advantage as a metric, but we can determine its significance if we define a reasonable value.

There are several methods to do so — I’ll explore this in a follow-up post. In the meantime, I’m going to list a few potential definitions we can explore:

• Quantify the number of combos in one player’s range over a certain equity threshold (e.g. the number of combos with greater than 80% equity on the flop)

• Quantify the number of combos at the top end of one player’s range that the other player does not have (e.g. if the best hand in our opponent’s range on a QJT flop is TT and we are uncapped, we have 22 better “nut combos” — we also have 16 combos of AK, 3 combos of QQ, and 3 combos of JJ)

• Quantify the number of actual nuts combos a player has

Since we haven’t formalized a definition, we will want to test all of these before determining what to utilize within our flop analysis.

Conclusion

It’s important to fully understand our overall data set, particularly our success metrics, as we start to explore this at scale. Now that each of these have been defined and we grasp which can be used for different scenarios, we can further explore the data set. In my next post, I plan to analyze the relationship between these variables and how we can utilize learnings from these interactions to influence our gameplay.

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